The line y = ½ x - 6 is being dilated by a scale factor of ½ from the center (4,4). What is the equation of the image?

Question

dilations

Answer 1

The y value of the line at x=4 is 0.5x-6 = -4. The distance grom 4 to -4 is 8. Dilate 8 by 1/2 and you get 4. Subtract 4 from 4 and you get 0.

The new y value at x=4 is 0.

The slope will remain the same.

y-(0) = 0.5(x-4)

y = 0.5x -2

y = (1/2)x -2

Here is a graph which shows the image line is now twice as "close" to the center of dilation as it was:

https://www.desmos.com/calculator/fytptvwc4c