Question

Find the equation of the line in slope-intercept form perpendicular to the line y= 3/2x-6 and passing through the point (9,-4)

Answer 1

y = -(2/3)x + 2

Explanation:

Perpendicular lines have slopes that are opposite reciprocals of each other. That means you take the slope, flip the fraction, and change the sign.

Here our given line is y = (3/2)x - 6 so the slope 5/9

The opposite reciprocal of 3/2 is -2/3

We set up the equation

y = -(2/3)x + b

we are given a point (x, y) of (9, -4), so plug that in and solve for b

-4 = -(2/3)(9) + b

-4 = -6 + b

2 = b

So our equation is y = -(2/3)x + 2