Question

Find the equation of the line perpendicular to y = - 4x + 8 that passes through the point (8,4).y =

Answer 1

Answer:

y= (1/4)x+2

Explanation:

Comparing y =-4x + 8 to the slope-intercept form y=mx+b

• Slope = -4.

Let the slope of the new line = m

Two lines are perpendicular if the product of their slopes is -1.

Therefore:

$\begin{gathered} -4m=-1 \\ m=\frac{-1}{-4} \\ m=\frac{1}{4} \end{gathered}$

The slope of the perpendicular line = 1/4

Since the line passes through the point (8,4), we have:

$\begin{gathered} y-y_1=m(x-x_1) \\ y-4=\frac{1}{4}(x-8) \\ y=\frac{1}{4}(x-8)+4 \\ y=\frac{1}{4}x-2+4 \\ y=\frac{1}{4}x+2 \end{gathered}$

The equation of the perpendicular line is y= (1/4)x+2