Question

Find the equation for the line that passes through the point (-2, 3), and that is perpendicular to the line with the equation x = -4.

Answer 1

The line with equation x=-4 passes parallel to the y axis. So, a line perpendicular to x=-4 is parallel to the x axis.

The slope of a line parallel to the x axis is m=0.

We have to find the equation of a line parallel to (x1, y1)=(-2, 3) and slope m=0.

Using point slope form of the equation of line, we get

`\begin{gathered} y-y1=m(x-x1) \\ y-3=0 \\ y=3 \end{gathered}`

Therefore, the equation for the line that passes through the point (-2, 3), and that is perpendicular to the line with the equation x = -4 is y=3.