Question

1Find an equation of the line perpendicular to the graph of yx + 5 that has a y-4intercept of (0, -3). Write your equation in slope-intercept form.

Answer 1

Given data:

The given equation of line is y=x/4+5.

The given y-intercept is (0,c)=(0,-3).

The standard equation of line is,

y=mx+c

Compare the given equation with the above expression.

m=1/4

The expression for the slope which is perpendicular to the given line.

$\begin{gathered} m^{\prime}\times m=-1 \\ m^{\prime}(\frac{1}{4})=-1 \\ m^{\prime}=-4 \end{gathered}$

The equation of the line which is perpendicular to the given line is,

$\begin{gathered} y=m^{\prime}x+c \\ =-4x-3 \end{gathered}$

Thus, the line which is perpendicular to the given line is y=-4x-3.