Question The line represented by 2y = x + 8 is dilated by a scale factor of k centered at the origin, such that the image of the line has an equation of y-1/2x=2. What is the scale factor?

The scale factor of the given dilation transformation is calculated as; 1/2 How to use the scale of dilation? We know that from transformation that a dilation is a non – rigid transformation that produces similar figures. If two lines are similar, then the lines are parallel and parallel lines always have the same slope. Thus; Line A has the formula; 2y = x + 8 Writing it in slope intercept form gives us; y = 0.5x + 4 ——(1) Thus; slope of the line A is m = 0.5 y-intercept of the line A is b = 4 Line B has the equation; y – ¹/₂x = 2 Rearranging in Slope Intercept form gives us; y = ¹/₂x + 2 Thus; slope of the line B is m = 0.5 y-intercept of the line B is b = 2 Now, it should be noted that the y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B. Thus; 4k = 2 k = 2/4 k = ¹/₂ Read more about Scale of Dilation at; https://brainly.com/question/10253650 #SPJ1 Reply

scale factorof the given dilation transformation is calculated as; 1/2## How to use the scale of dilation?

non – rigid transformationthat produces similar figures.paralleland parallel lines always have thesame slope.slopeof the line A is m = 0.5y-interceptof the line A is b = 4Slope Intercept formgives us;slopeof the line B is m = 0.5y-interceptof the line B is b = 2scale factork must be equal to the y-intercept of line B. Thus;Scale of Dilationat; https://brainly.com/question/10253650