Question

The line given by -18x+7y= -21 is dilated by a scale factor of k=3, centered at the origin. What is an equation of the image of the line after dilation?

Answer 1

Given the following line

`-18x+7y=-21`

We want to know the image of a dilation with a scale factor of 3 centered at the origin.

When we dilate a line, we basically tarnslated that line. The slope stays the same and we change the y-intercept. Since this dilation is centered at the origin, we just need to multiply the y-intercept by the scale factor. Since our equation is written in standard form, this is the same as multiplying the right side of the equation by the scale factor.

`\begin{gathered} -18x+7y=-21\cdot k \\ k=3\Rightarrow-18x+7y=-21\cdot3 \end{gathered}`

Then, our image is

`-18x+7y=-63`