Question

Find an equation for the line that passes through the points (-6, 3) and (6, -6).

Answer 1

slope=-9/12 = -3/4

y=mx+b y=-3/4x+b

3=-3/4(-6)+b

b=3+9/2=7.5

Equation is y=-0.75x+7.5

Answer 2

`y = -(3)/(4)x-(3)/(2)`

Explanation:

First, calculate the slope of the line:

`m = (y_2-y_1)/(x_2-x_1)\\m = ((-6) - 3)/(6 - (-6))\\m = (-9)/(12)\\m = (-3)/(4)`

Next, calculate the y-intercept:

Choose any point on the line.

`(-6,3)`

Solve for
`b`.

`y = mx + b\\b = y - (mx)\\b = 3 - ((-3)/(4) * -6)\\b = 3 - (9)/(2)\\b = (-3)/(2)`

Finally, create the equation:

`y = -(3)/(4)x-(3)/(2)`