Question

Find the equation of the line that passes through (-4, 2) and is perpendicular to the line that goes through (-4, 6) and (5, 2).

Answer 1

9x -4y = -44

Explanation:

You want the equation of the line through (-4, 2) and perpendicular to the line through (-4, 6) and (5, 2).

Equation of a Line

The equation of a line through (h, k) and perpendicular to the line through (x1, y1) and (x2, y2) can be written as ...

(x2 -x1)(x -h) +(y2 -y1)(y -k) = 0

Using the given points, this becomes ...

(5 -(-4))(x -(-4)) +(2 -6)(y -2) = 0

9(x +4) -4(y -2) = 0

Expanding this gives the general form equation:

9x -4y +44 = 0

Subtracting the constant gives the standard form equation:

9x -4y = -44