Question

What is the equation of the line that passes through points (2, −6) and (−4, 3)?

Answer 1

y = -1.5x - 3

Explanation:

Find the slope using rise over run, (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are points on the line

Plug in the points:

(y2 - y1) / (x2 - x1)

(3 + 6) / (-4 - 2)

9 / -6

3/-2 or -1.5

Then, plug in the slope and a point into y = mx + b to find b:

y = mx + b

-6 = -1.5(2) + b

-6 = -3 + b

-3 = b

Plug in the slope and b into y = mx + b

y = -1.5x - 3 is the equation

Answer 2

y = -3/2x - 3

Explanation:

Slope-Intercept Form: y = mx + b

Slope Formula:
`m=(y_2-y_1)/(x_2-x_1)`

Step 1: Find slope m

`m=(3-(-6))/(-4-2)`

`m=(3+6)/(-6)`

`m=(9)/(-6)`

`m=(-3)/(2)`

y = -3/2x + b

Step 2: Find y-intercept b

3 = -3/2(-4) + b

3 = 6 + b

b = -3

Step 3: Rewrite linear equation

y = -3/2x - 3