Question

A line passes through the point (-9,3) and has a slope of -2/3?
Write an equation in point slope for this line.

Answer 1

The point-slope form:

$y-y_1=m(x-x_1)$

We have the slope m = -2/3 and the point (-9, 3). Substitute:

$y-3=-\dfrac{2}{3}(x-(-9))$

$y-3=-\dfrac{2}{3}(x+9)$      use distributive property

$y-3=-\dfrac{2}{3}x-\dfrac{2}{3}\cdot9$

$y-3=-\dfrac{2}{3}x-(2)(3)$

$y-3=-\dfrac{2}{3}x-6$     add 3 to both sides

$\boxed{y=-\dfrac{2}{3}x-3}$