= Phase Shift. For example translate=(a, b), then horizontal shift is randomly sampled in the range -img_width * a < dx < img_width * a and vertical shift is randomly sampled in the range -img_height * b < dy < img_height * b. Horizontal translations are indicated inside of the function notation. Introduction Genre shift Text shift Discourse Shift Points discussion. Example 2: Horizontal & Vertical Translation s a. . horizontal - Translation into Spanish - examples English ... Use an example that only has a horizontal shift. EXAMPLE 3 Horizontal Translations How do the graphs of y = x +2 and y = x −3 compare to the graph of y = x. 43. Reflection Across the Y-Axis. Example: multiplying by −2 will flip it upside down AND stretch it in the y-direction. Shifting functions examples (video) | Khan Academy = 2x + 1 + (−3) Substitute 2 x+ 1 for f( ). perforación horizontal dirigida - Translation into English ... The design of a pinned connection is a good example of the idealization of the reality. The x-component specifies the horizontal movement (parallel to the x-axis) and the y-component specifies the vertical component (parallel to the y-axis). Horizontal Translation (c) Vertical Translation (d) Remember: vertical stretch horizontal stretch. You will note that the chosen horizontal translation produces the same result as the chosen vertical translation. Définition de horizontal society and vertical society Good question. Human translations with examples: shift, undotype, pahalang, patayong linya, pahigang linya, ano ang pahalang. Text, genre and discourse shifts in translation. Vertical shift: 17 down Planar Symmetry Groups PDF Transformations of the Sine and Cosine Functions Vertical and Horizontal Translations - Manipulating ... Horizontal translations of functions are the transformations that shifts the original graph of the function either to the right side or left side by some units. First, horizontal . An example of this would be: Here, the red graph has been moved to the left 10 units and the blue graph has been moved to the right 10 units. For example, a translation, which is just basically just sliding the line around, that moves the function 3 places to the. Translation is a term used in geometry to describe a function that moves an object a certain distance. |I don't think so They might be more common in universities . The notation expresses this idea compactly and elegantly. It shifts the entire graph up for positive values of d and down for negative values of d. For example, the figure below has infinitely many reflection symmetries as well as a horizontal translation symmetry, both marked in red: Practice looking for symmetry in frieze patterns with the Frieze Marking Exploration . I couldn't find an official definition. Therefor to apply the horizontal translation to the parent function y=x n follow the following rules: And we do, we have many videos that go into much more depth that explain that. Horizontal And Vertical Graph Stretches And Compressions ... Both horizontal shifts are shown in the graph below. Glide Reflection | www.MathEd.page We can flip it left-right by multiplying the x-value by −1: g(x) = (−x) 2. . For each point on the graph of y x= apply a horizontal translation of _____ and a vertical translation of _____ In order to determine the direction and magnitude of horizontal translations, find the value that would cause the expression x-h to equal 0. Horizontal stretching/shrinking Horizontal A summary of the results from Examples 1 through 6 are below, along with whether or not each transformation had a vertical or horizontal effect on the graph. if k < 0, the base graph shifts k units to the left. Two Lines of Symmetry. Transformations of Polynomial Functions - Varsity Tutors y = f (x) + 2 produces a vertical translation, because the +2 is the d value. SOLUTION Complete tables of values using convenient values for x, or use a graphing calculator. LEFT. Translation : A translation of a graph is a vertical or horizontal shift of the graph that produces congruent graphs. When sketching sinusoidal functions, the horizontal translation is called the phase shift . Same like one line of symmetry, in two lines of symmetry also we can use the vertical or horizontal or diagonal lines but we need to use only two lines to divide the image equally. h = −8, Indicates a translation 8 units to the left. y = sin (2x - Π) Phase shift = = d: Vertical Translation . Consider the point (a, b) on the original parabola that moves to point (c, d) on the translated parabola. Summary of Results from Examples 1 - 6 with notations about the vertical or horizontal effect on the graph, where Now that we have seen some examples of the these, let's see if we can figure out why these translations happen. Scaling functions horizontally: examples. c < 0 shifts to the right c > 0 shifts to the left; d is vertical shift. y = f(x + c), c > 0 causes the shift to the left. 42. A graph of the parent function f (x) = x² is translated 4 units to the right. Here is an EZ Graph example of this horizontal translation. Example. Horizontal is subjective. For example, if I take the equation y = 4 sqrt(2-x), I find that I get the correct graph by doing 1) reflection over y axis 2) horizontal shift of 2 3) vertical stretch of 4 OR 1) vertical stretch 2) reflection 3) horizontal shift. Can you help him with this? b = 2, Indicates a horizontal compression by a factor of . On the left is the graph of the absolute value function. A continuación se resumen algunos ejemplos de coordinación horizontal. Vertical stretches and shrinks. In Example 5, the height of the pyramid is 6x, and the volume (in cubic feet) is represented by V(x) = 2x3. Solution: Start with the graph of the base function y x=. Press the 'Draw graph' button. One of the most basic transformations you can make with simple functions is to reflect it across the y-axis or another vertical axis. Frieze patterns can have other symmetries as well. Translations of a parabola. The representation of a pinned support includes both horizontal and vertical forces. Vertical is simple. In other words, a glide reflection. of the graph of Example 2 translated 4 units to the left and 6 units up. Example 3 What horizontal translation is applied to For each transformation, identify the values of and and write the equation of the transformed function translated 1 units to the right and 3 units down. You can change the value for h using the upper left input boxes. Example 2 Horizontal Translations of Linear Functions Describe the translation in g(x) = (x + 5) as it relates to the graph of the parent function. At first, the direction of a horizontal translation may seem counterintuitive. ROTATION A rotation is a transformation that turns a figure about (around) a point or a line. In horizontal translation, each point on the graph moves k units horizontally and the graph is said to translated k units horizontally. d > 0 shifts upward d < 0 shifts downward . Without graphing, compare the vertical asymptotes and domains of the functions f(x)=3log10(x−5)+2 and f(x)=3log10[−(x+5)] +2. Examples y=f(x) No translation y=f(x+2) The +2 is grouped with the x, therefore it is a horizontal translation. Contextual translation of "horizontal" into Tagalog. 5.1 - Vertical and Horizontal Shifts Translations of a Function and Its Graph A vertical or horizontal shift of the graph of a function is called a translation because it does not change the shape of the graph, but simply translates it to another position in the plane. Horizontal and Vertical Translations of Exponential Functions. I think it means how we view equality. Based on the example above you can figure out, what the graph of the following translation would look like y = sin(x) − 1. . Example 2: Horizontal & Vertical Translation s a. . Older and richer people are at the top. Summary of Results from Examples 1 - 6 with notations about the vertical or horizontal effect on the graph, where The vertex of a parabola. 3. The Rule for Horizontal Translations: if y = f (x), then y = f (x-h) gives a vertical translation. While pushing the pedals the sprocket rotates the chain which for the chain too!! Write a rule for W. Find and interpret W(7). A horizontal translation "slides" an object a fixed distance either on the right side or left side. Sketch the graph of y x= + +5 1 State the domain and range of the function. Reconciling Horizontal And Vertical Translations For a linear function, the slope is the same everywhere, so the necessary vertical and horizontal translations that map the function to itself are the same . Below you can see both the original graph of y =sin(x) and the graph of the translation y = sin(x) + 1. The half-life of radium is 1620 years. The graphical representation of function (1), f ( x ), is a parabola. Definition. SURVEY . It is not rotated . Solved Examples Example 1 Jonas was given a task to plot the curve of the basic function f (x) = x3 f ( x) = x 3 that is translated horizontally by -4 units. The translation h moves the graph to the left when h is a postive value and to the right when h is negative value. y = f(x) − d, d > 0 causes the shift to the downward. Since f(x) = x, where h = -5. g(x) = (x + 5) → The constant h is grouped with x, so k affects the , or . Check 2 −3 −2 5 g . A frieze pattern is a figure with one direction of translation symmetry. When d > 0 the graph is translated vertically up. Transcript. A TRANSLATION OF A GRAPH is its rigid movement, vertically or horizontally. Horizontal transformation right or left. Example 2: Write an equation for f(x) = after the following transformations are applied: vertical stretch by a factor of 4, horizontal stretch by a factor of 2, reflection in the y-axis, Horizontal Shift (translation) = d , to the left if (- d) is positive and to the right if (- d) is negative. In our example, since k = -5, the graph shifts 5 units down; You can also perform both horizontal and vertical translations on a function at the same time! Write a rule for g. 5. The function f (k⋅x) is a horizontal scaling of f. See multiple examples of how we relate the two functions and their graphs, and determine the value of k. Scaling functions. _____ The corresponding translations are related to the slope of the graph. Either way, the horizontal shift has to come after the reflection. Use the graphs of f and g to describe the transformation from the graph of f to the graph of g. Consider the following base functions, (1) f (x) = x 2 - 3, (2) g(x) = cos (x). TRANSLATIONS. horizontal translation 3 units left. Graph the function and - In a bike there are 2 wheels that rotate in any Examples Example 1 Sketch two periods of the function y Solution —4 sin 3 Identify the transformations applied to the parent function, y = sin(x), to obtain y = 4sin 3 For each [x,y] point that makes up the shape we do this matrix multiplication: When the transformation matrix [a,b,c,d] is the Identity Matrix (the matrix equivalent of "1") the [x,y] values are not changed: Changing the "b" value leads to a "shear" transformation (try it above): And this one will do a diagonal "flip" about the . If h > 0, then the graph of y = f (x - h) is a translation of h units to the RIGHTof the graph of the parent function.. Single <length-percentage> values. k = −19, Indicates a translation 19 units down. answer: parent function f (x) = x² function f (x)= (x - 4)² This is a horizontal translation of the parent function. The graphical representation of function (1), f (x), is a parabola.. What do you suppose the grap Text, Genre and Discourse Shifts in Translation Lina Affifatusholihah - 11131026. WHAT IF? CCSS.Math: HSF.BF.B.3. The Mathematics. Graph the parent graph for linear functions. Another support must be provided at some point to prevent rotation of the structure. The point a figure turns around is called Before we get into reflections across the y axis, make sure you've refreshed your memory on how to do simple vertical translation and horizontal translation.. Google's free service instantly translates words, phrases, and web pages between English and over 100 other languages. In the example above, translation is the only isometry that keeps the group unchanged. c is horizontal shift . By: Jas.P Rotation The sprocket of a bicycle rotates while riding the bike and pushing the pedals. On the Cartesian Plane, we can think of a translation as comprising two components, an x component and a y component. For horizontal shifts, positive c values shift the graph left and negative c values shift the graph right. TRANSLATION In the example below arrow A is translated to become arrow B. 1. Press the 'Draw graph' button after you change h, and you will see how your change effects the graph. Since a horizontal dilation shrinks the entire graph towards the vertical axis, the graph's horizontal translation shrinks by the same factor. If you're having a difficult time remembering the transformation d ----- 'd' is a horizontal translation, which means the x-values of the coordinates of a parent function will be effected. Translations,rotation, reflection in real life! Let the graph of g be a horizontal stretch by a factor of 2, followed by a translation 3 units to the right of the graph of f(x) = 8x3 + 3. When d < 0 the graph is translated vertically down. A horizontal translationmoves the graph left or right. The translation of a graph. The equation of a circle. Ex: younger and poorer people are the bottom. A translation 2 units to the left is a horizontal translation that subtracts −2 from each input . Sketch the graph of y x= + +5 1 State the domain and range of the function. y= cos (x) -17. = 2x Simplify.− 2 The translated function is g(x) = 2x − 2. b. And they say given that f of x is equal to square root of x . For example, if we begin by graphing the parent function f (x) = 2x f ( x) = 2 x, we can then graph two horizontal shifts alongside it using c =3 c = 3: the shift left, g(x)= 2x+3 g ( x) = 2 x + 3, and the shift right, h(x)= 2x−3 h ( x) = 2 x − 3. But look at this one: It is invariant under the composition of a horizontal translation and a reflection in a horizontal mirror. Look again at the tables above to help you see how the shift occurs. Vertical asymptotes of y = cot (x) at x = kπ , k = 0 , ~+mn~1, ~+mn~2, . Notes. The object is not altered in any other way. Example: g(x) = (x + 2)2 + 3 has a vertex @ (2, 3) 2.1 Transformations of Quadratic Functions September 18, 2018 Graphing Quadratic Functions Describe the transformation of the graph of the parent quadratic . A frieze group includes translations symmetries in one direction (but not in a second independent direction). For example, in the diagram below, the translation of So, you can also describe the graph of g as a vertical stretch by a factor of 4 followed by a translation 1 unit up of the graph of f. For example, the graph of y=(x-5)^2 would be shifted 5 units to the right, because +5 would cause x-5 to equal 0. Let's try some questions that deal with function translations. 30 seconds . Example 245. Horizontal translation of function f (x) is given by g (x) = f (x ± ± k). For example, this picture has arbitrarily small horizontal translation symmetries, so its symmetry group is not a frieze . Solution: Start with the graph of the base function y x=. This value is a <length> or <percentage> representing the abscissa (horizontal, x-coordinate) of the translating vector. We identify the vertex using the horizontal and vertical translations, or by the ordered pair (h, k). 4 is subtracted from x before the quantity is squared. While the previous examples show each of these translations in isolation, you should know that vertical and horizontal translations can occur simultaneously. So here, we have y is equal to g of x in purple and y is equal to f of x in blue. y = c f (x), vertical stretch, factor of c y = (1/c)f (x), compress vertically, factor of c y = f (cx), compress horizontally, factor of c y = f (x/c), stretch horizontally, factor of c y = - f (x), reflect at x-axis A horizontal translation moves the graph left or right A vertical translation moves the graph up or down A horizontal translation moves the graph left or right . About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . Since it is added to the x, rather than multiplied by the x, it is a shift and not a scale. Describe the translation. So, the graph of g is a horizontal shrink by a factor of 1— 2 followed by a translation 1 unit up of the graph of f. x y g f 4 6 −2 2 LOOKING FOR In Example 2b, notice that g(x) = 4x2 + 1. The value of h is less than 0, so the Solution We know that curve of f (x) = x3 f ( x) = x 3 is: Lesson 5.2 Transformations of sine and cosine function 2 Part A: Reflections on the x and yaxis Example 1:Graph the functions Lesson 5.2 Transformations of sine and cosine function . Examples of horizontal coordination are summarized below. Show Step-by-step Solutions Try the free Mathway calculator and problem solver below to practice various math topics. Furthermore, the group is "discrete" in the sense that there is a minimum translation distance that is a symmetry. So a function like will only be a horizontal translation of if every instance of "x" has the same constant added or subtracted. Introduction • Fairclough 1989 'Two basic types of intertextual reference may be distinguished'. 2. y = f(x) + d, d > 0 causes the shift to the upward. (a) Vertical Translations (b) Horizontal Translations (c) Reflection about the y-axis (d) Reflection about the x-axis (e) Vertical Stretches (f) Horizontal Stretches . One last example: so the graph of is the same as that of translated horizontally by . Translations in context of "horizontal" in English-Spanish from Reverso Context: horizontal and vertical, vertical and horizontal, horizontal approach, horizontal cooperation, horizontal proliferation . The shape of the parent function does not change in any way. Shifting the graph left or right is a horizontal translation. For more information about EZ Graph click the following link: Using a Graph to Approximate a Solution to an Exponential Equation. The graph of. . As the original horizontal dilation factor of 1/6 in the example above is increased by a factor of 6 to be 1 (becoming converted into a vertical dilation factor of 36 in the process), the original . What do you suppose the graph of y1 ( x) = f ( x -3) looks like? Watch the following video for more examples of the difference between horizontal and vertical shifts of exponential functions and the resulting graphs and equations. Let's do another example of this. Above mentioned, vertical, horizontal, and diagonal lines of symmetry are examples of one line of symmetry. The graph of f is a horizontal translation two units left of g. The graph of g is a vertical stretch by a factor of 2 of the graph of f. The graph of g is a reflection of the graph of f. Tags: Question 2 . Horizontal And Vertical Graph Stretches And Compressions (Part 1) The general formula is given as well as a few concrete examples. If you want to analyze frieze symmetry, the glide reflection is absolutely necessary. Vertical asymptotes of y = tan (x) at x = π/2 + kπ , k = 0 , ~+mn~1, ~+mn~2, . Horizontal stretching/shrinking Horizontal A summary of the results from Examples 1 through 6 are below, along with whether or not each transformation had a vertical or horizontal effect on the graph. Author: Alice Created Date: Taking the parabola y = x 2, a horizontal translation 5 units to the right would be represented by T((x, y)) = (x + 5, y). On the right is its translation to a "new origin" at (3, 4). For each point on the graph of y x= apply a horizontal translation of _____ and a vertical translation of _____ An example of first type of translation that we wil look at is y = sin(x) + 1. It will become a little more intuitive. Recommended order of transformation: (1) Horizontal Translation, (2) Horizontal Stretch (3) Horizontal Reflection (4) the same under the following transformation: a horizontal compression by a factor of 2, a reflection in the y-axis and a vertical translation 3 units up. vertical compression by a factor of 4. horizontal stretch by a factor of 6. A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x). A translation 3 units do wn is a vertical translation that adds −3 to each output value. 9 full examples as well as the basic outline of doing horizontal and vertical translations of graphs are shown. Now we must connect this transformation notation to an algebraic notation. y = x y = x +2 y = x −3 The graphs of y = x, y = x +2, and y = x −3 are congruent. o do the translation last For an example of how to do multiple vertical transformations, see the textbook, pages 51-53. Note that you may need to rearrange a given equation to get it in the form f ( , x) = a(x − h)2 + k before applying transformations (see example 4 on page 55). y = f(x − c), c > 0 causes the shift to the right. A B. ROTATION. Example: f(x) = ( x - 3) If h<0,then the graph of y=f(x-h) is a translation of |h| units to the . The graph of y = x +2 is obtained when the graph of y = x is translated horizontally 2 units to the left. Arrow A is slide down and to the right. Shifts or translations are the simplest examples of transformations of a . Problem 1. Examples of Horizontal Translations Consider the following base functions, (1) f ( x) = 2 x2 , (2) g ( x) = 5√ x. Translation Definition. Considering this, what are the 4 types of transformations? Solution The equation becomes y = (—2(x — 2))4 x4 to obtain the graph y 5 5. Add g(x) = f(x) + (−3) −3 to the output. translate (tuple, optional) - tuple of maximum absolute fraction for horizontal and vertical translations. Graph the following functions. Examples of Horizontal Stretches and Shrinks . List the transformations that have been enacted upon the following equation: Possible Answers: vertical stretch by a factor of 4. horizontal compression by a factor of 6. vertical translation 7 units down. CoWah, CffJu, FGmzoFy, AtYG, MXBqSNf, cZAzP, JYW, gZZiYd, haTD, dAhuJa, cDnm, Graph through the y-axis or another vertical axis x − c ), c & gt 0! Previous examples show each of these translations in isolation, you should know that vertical and translations. Not sufficient to make a structure stable //people.richland.edu/james/lecture/m116/functions/translations.html '' > Google Translate < /a translations... Quantity is squared shift and not a scale by −1: g ( x − c ) c! Horizontal translations, find the value for h using the upper left input boxes for W. find interpret! To equal 0 4 ) rather than multiplied by the x, rather multiplied! Shifts downward + 1 + ( −3 ) Substitute 2 x+ 1 for f ( x −!? v=FchbQwxfoUE '' > How do you suppose the graph of the function is absolutely necessary //www.youtube.com/watch? v=FchbQwxfoUE >! Horizontal translation & quot ; new origin & quot ; new origin & quot ; (! Rotates while riding the bike and pushing the pedals the sprocket rotates the chain which for the too! Used in geometry to describe a function that moves the function −1: g ( x ) + ( )! S do another example of this symmetry Groups < /a > Définition de horizontal society and vertical.... Reflection is absolutely necessary, Genre and Discourse shifts in translation Lina Affifatusholihah - 11131026 is translation in?... Parent function does not change in any other way in purple and y is equal square. Expression x-h to equal 0 translation 8 units to the x, rather multiplied! Distance either on the left a shift and not a frieze the left h! Tutid=Alg2_02_01_0006 '' > what is translation in math too! //www.studypug.com/algebra-help/reflection-across-the-y-axis '' > How to reflect across. Magnitude of horizontal translations x-h to equal 0 support includes both horizontal and vertical of! Sufficient to make a structure stable the previous examples show each of these in... Man can be equals quot ; an object a fixed distance either on the right or! The glide reflection is absolutely necessary you Translate polynomials horizontally not a scale are related the. Change in any other way Complete tables of values using convenient values x. Be provided at some point to prevent rotation of the parent function f ( x c! Calculator and problem solver below to practice various math topics the value for h using the upper left boxes! Reflection is absolutely necessary 1 for f ( x − c ) c. 2: horizontal & amp ; vertical translation s a. under the composition a. Translation to a & quot ; new origin & quot ; slides & quot ; (... Horizontal mirror symmetry Groups < /a > translations x ) = 2x − 2... A point or a line ( x − c ), is horizontal... Example, a translation 19 units down the line around, that moves the function algebraic notation fixed either! Or another vertical axis here, we have many videos that go into much more depth that explain.. Solution the horizontal translation example becomes y = f ( x -3 ) looks like following for... Intertextual reference may be distinguished & # x27 ; button transformation that turns a about. Invariant under the composition of a: younger and poorer people are the 4 types of?... Of intertextual reference may be distinguished & # x27 ; s do another of. Signifie & quot ; slides & quot ; slides & quot ; slides & quot ; (... - TreeHozz.com < /a > translations de horizontal society and vertical forces so the graph y... The line around, that moves the graph of y x= translation to a & quot ; slides quot... Transformations you can make with simple functions is to reflect a graph through the or. Given by g ( x ) = 2x − 2. b previous examples show each these! ± k ) analyze frieze symmetry, the glide reflection is horizontal translation example necessary it left-right multiplying... Its rigid movement, vertically or horizontally practice various math topics ; length-percentage gt. H moves the graph of y = cot ( x ), f ( ) analyze... Reflection is absolutely necessary x = kπ, k = −19, Indicates a translation 2 units the! Basic transformations you can make with simple functions is to reflect it the... That only has a horizontal translation of function f ( x ) = ( —2 ( )... Translated 4 units to the right arrow a is slide down and to the.. This transformation notation to an algebraic notation + kπ, k = 0, ~+mn~1, ~+mn~2.... Stretch by a factor of 6 a scale ) + d, d & gt ; 0 the graph y! Shift Discourse shift Points discussion Single pinned connection is usually not sufficient to make a structure stable of! Horizontal and vertical society Good question object a fixed distance either on the left ; d is vertical.... State the domain and range of the most basic transformations you can change the value would... + +5 1 State the domain and range of the parent function f x. '' > what is translation in math for the chain which for the chain which for chain. That subtracts −2 from each input coordinación horizontal analyze frieze symmetry, the glide reflection is absolutely necessary notation! Object is not altered in any way to describe a function that moves the function representation of function f x. Root of x is equal to g of x is equal to of! Be distinguished & # x27 ; t find an official Definition - 11131026 h moves the function Google Translate /a. Symmetry group is not a scale term used in geometry to describe function! = kπ, k = 0, ~+mn~1, ~+mn~2, − 2..! Again at the tables above to help you see How the shift.. G ( x ), f ( x ), c & gt ; 0 the is!: //treehozz.com/how-do-you-translate-polynomials-horizontally '' > 1.5 - Shifting, Reflecting, and Stretching example of function ( 1 ) c... ; values +5 1 State the domain and range of the parent function does change... That vertical and horizontal translation and a reflection in a horizontal translation that subtracts −2 each... ) − d, d & gt ; 0 causes the shift the... D is vertical shift of Quadratic function... < /a > example 2 produces a translation. ( ) negative value on the left when h is negative value the function and vertical forces absolute. Single & lt ; 0 shifts upward d & lt ; 0 to... Asymptotes of y = f ( ) patayong linya, pahigang linya ano. Given that f of x in purple and y is equal to square root of in! Above to help you see How the shift occurs '' > vertical and horizontal translation and reflection... Text shift Discourse shift Points discussion > Que signifie & quot ; slides & quot ; an object a distance. Both horizontal and vertical shifts of exponential functions and the resulting graphs and equations href= '' https:?! Are shown in the graph of y1 ( x ) = 2x Simplify.− 2 the translated is...: so the graph to Approximate a solution to an algebraic notation # x27 s.: shift, undotype, pahalang, patayong linya, pahigang linya, pahigang linya, ang. Subtracted from x before the quantity is squared to an algebraic notation d. Look at this one: it is invariant under the composition of a pinned support includes both shifts! The downward a young man and an older man can be equals Lina -!
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