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)=-(1)/(m)`

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

`\begin{gathered} m^(\prime)=-(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.