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 (-1, 6) and (3, -2). Substitute:
[tex]m=\dfrac{-2-6}{3-(-1)}=\dfrac{-8}{4}=-2\\\\y-6=-2(x-(-1))\\\\y-6=-2(x+1)\qquad\text{use distributive property}\\\\y-6=-2x-2\qquad\text{add 6 to both sides}\\\\y=-2x+4\qquad\text{add 2x to both sides}\\\\2x+y=4[/tex]
Answer:
y - 6 = -2(x + 1) point-slope form
y = -2x + 4 slope-intercept form
2x + y = 4 standard form
