The point-slope form:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, -5) and (6, -2). Substitute:
[tex]m=\dfrac{-2-(-5)}{6-(-3)}=\dfrac{-2+5}{6+3}=\dfrac{3}{9}=\dfrac{1}{3}\\\\y-(-5)=\dfrac{1}{3}(x-(-3))\\\\y+5=\dfrac{1}{3}(x+3)\qquad\text{use distributive property}\\\\y+5=\dfrac{1}{3}x+1\qquad\text{subtract 5 from both sides}\\\\y=\dfrac{1}{3}x-4\qquad\text{multiply both sides by 3}\\\\3y=1x-12\qquad\text{subtract x from both sides}\\\\-x+3y=-12\qquad\text{change the signs}\\\\x-3y=12[/tex]
Answer:
point-slope form: y + 5 = 1/3(x + 3)
slope-intercept form: y = 1/3 x + 12
standard form: x - 3y = 12
