If the line represented by y = 1/2x - 3 is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?

Answer 1

While it would help to know what the possible statements are, think of it like this:

Dilation of a line using a certain center just means the line is moving a certain scale factor away from that center point. Typically, dilations of lines will maintain the same slope, but the y-intercept (and thereby the x-intercept) are going to be r times farther away. You’re already given the equation in slope intercept form, so multiply your y intercept (-3) by your scale factor (4) and you have your new y-intercept (-12). Presuming your slope stays the same, your new x-intercept will occur where y=0 for the equation y = 0.5x - 12.