Question

What equation represents the line that passes through the points (-3,7) and (9,-1)

Answer 1

The point-slope form:

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

m - slope

(x₁, y₁) - point

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-3, 7) and (9, -1). Substitute:

$m=\dfrac{-1-7}{9-(-3)}=\dfrac{-8}{12}=-\dfrac{2}{3}$

$y-7=-\dfrac{2}{3}(x-(-3))\\\\\boxed{y-7=-\dfrac{2}{3}(x+3)}$      point-slope form

$\boxed{y=-\dfrac{2}{3}x+5}$        slope-intercept form

$\boxed{2x+3y=15}$       standard form