Question

5 $y = 4x - 2$ is dilated by a scale factor of 2 with the center as the $(-1, -6)$. will the two lines be parallel, perpendicular, same line, or no relationship? what is the equation of the new line?

Explanation:

Step1: Check if the center of dilation is on the original line

Substitute \(x = - 1\) into \(y=4x - 2\): \(y=4\times(-1)-2=-4 - 2=-6\). So, the point \((-1,-6)\) lies on the line \(y = 4x-2\).

Step2: Determine the equation of the dilated line

When a line is dilated about a point on the line, the line remains the same. So the equation of the new line is \(y = 4x-2\)

Answer:

\(y = 4x - 2\)