Question

Write an equation for the line perpendicular to line XY that contains point Z.

line XY: 3x + 2y = -6, Z(3,2)

I realize that the slope of a perpendicular line is the opposite reciprocal of the first line. But, how do I use point Z in this problem? Thank you.

Answer 1

y= -3/2x-3
so the new slope will be 2/3
so then y=2/3 x+b
put point z into the equation, and solve for b.

Answer 2

Since you know that the slopes of perpendicular lines are opposite reciprocals, you should accept that the new equation must be
2x - 3y = c
plug in the point
6 - 4 = c = 2

so 2x - 3y = 2