The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, 7) and (9, -1). Substitute:
[tex]m=\dfrac{-1-7}{9-(-3)}=\dfrac{-8}{12}=-\dfrac{2}{3}[/tex]
[tex]y-7=-\dfrac{2}{3}(x-(-3))\\\\\boxed{y-7=-\dfrac{2}{3}(x+3)}[/tex] point-slope form
[tex]\boxed{y=-\dfrac{2}{3}x+5}[/tex] slope-intercept form
[tex]\boxed{2x+3y=15}[/tex] standard form
