First, students will gain an intuition of dilating lines by playing with this Geogebra interactive. Here's a video which might help you figure out what questions to ask, to guide your students on their discovery. Then students will learn how to dilate lines. One type of problem, is to provide two lines, then ask for a center and scale factor that would map one of the lines onto the other. Here's an example. Another type of problem, is to provide the equation of a line, in slope-intercept form, the center of dilation, and the scale factor. From here, the task is to find the equation of the dilated line. Here's a video on that.