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 (6, 8) and (-3, 2). Substitute:
[tex]m=\dfrac{2-8}{-3-6}=\dfrac{-6}{-9}=\dfrac{2}{3}\\\\y-8=\dfrac{2}{3}(x-6)\qquad|\text{use distributive property}\\\\y-8=\dfrac{2}{3}x-4\qquad|+8\\\\y=\dfrac{2}{3}x+4\qquad|-\dfrac{2}{3}x\\\\-\dfrac{2}{3}x+y=4\qquad|\cdot(-3)\\\\2x-3y=-12[/tex]
Answer:
point-slope form: [tex]y-8=\dfrac{2}{3}(x-6)[/tex]
slope-intercept form: [tex]y=\dfrac{2}{3}x+4[/tex]
standard form: [tex]2x-3y=-12[/tex]
