Question

Write the equation of the line that goes through each set of points (-1,6),(3-2)

Answer 1

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-1, 6) and (3, -2). Substitute:

$m=\dfrac{-2-6}{3-(-1)}=\dfrac{-8}{4}=-2\\\\y-6=-2(x-(-1))\\\\y-6=-2(x+1)\qquad\text{use distributive property}\\\\y-6=-2x-2\qquad\text{add 6 to both sides}\\\\y=-2x+4\qquad\text{add 2x to both sides}\\\\2x+y=4$

Answer:

y - 6 = -2(x + 1)    point-slope form

y = -2x + 4      slope-intercept form

2x + y = 4     standard form