Question

Line p is perpendicular to the line y=1/4x-3 and passes through (-8,2). line m is the image of line p Dilated centered at the origin with scale factor of 2/5. What is the equation of line m?

Answer 1

Explanation:

First we have to find the equation of line p, which is perpendicular to y=1/4x - 3, therefore its slope is reciprocal and opposite to the given line:

$y_p=-4x+b$

To find the y-intercept b we have to use the point. Replace x = -8, y = 2 and solve for b:

$\begin{gathered} 2=-4(-8)+b \\ 2=32+b \\ b=2-32 \\ b=-30 \end{gathered}$

The equation of line p is:

$y_p=-4x-30$

Now, line m is a dialation of line p centered at the origin, so the slope doesn't change - this means that line m is parallel to line p - and the y-intercept is the product of the y-intercept of line p by the scale factor:

$\begin{gathered} y_m=-4x-30\cdot\frac{2}{5} \\ y_m=-4x-12 \end{gathered}$

Answer:

The equation of line m is y = -4x - 12