Question

How do you find a standard form equation for the line with point (2, 5) and is perpendicular to the line 4x + 9y − 7?

Answer 1

9x - 4y + 2 = 0

Explanation:

Given line is 4x + 9y - 7 = 0.
or, 9y = - 4x + 7
or, y = - 4x/9 + 7/9 . It's slope is - 4/9.

Let m be the slope of the perpendicular line.
Then, m x ( - 4/9 ) = - 1
Hence m = 9/4

Let the required equation be y = 9/4 x + c. Since it passes through
(2 , 5), we get c = 5 - 9/2 = 1/2.

The equation is y = 9/4 x + 1/2
or, 4y = 9x + 2
or, 9x - 4y + 2 = 0