Question

write the equation of the line perpendicular to y=-X-3 that passes through the point (4,-1).

Answer 1

The general equation of line is y=mx+b. The equation of line is y=-x-3, which has slope of m=-1.

The formula for the slope of perpendicular line is,

$m^{\prime}=-\frac{1}{m}$

Substitute -1 for m in the equation to obtain the slop of perpendicular line.

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

The equation of line passes through point (x_1,y_1) with slope m' is,

$y-y_1=m^{\prime}(x-x_1)$

Substitute the points and slope in the equation to determine the equation of the perpendicular line.

$\begin{gathered} y-(-1)=1(x-4) \\ y+1=x-4 \\ y=x-5 \end{gathered}$

So equation of perpendicular line is, y=x-5.