Which of the following is an equation of the line through (2, 3) and (−1, −12)? A. y = 15x + 135
B. y = −15x + 175
C. y = 5x − 7
D. y = −5x + 7

First, we have two points and we need to use these points to find the slope. To do this, let's label one point x1 and y1, the other point x2 and y2 then,

Slope = (y2 - y1) / (x2 - x1)

(2, 3) - 2 is x1 and 3 is y1

(-1, -12) -1 is x2 and -12 is y2

Slope = (-12 - 3) / ( -1 - 2) = -15 / -3 = 5

Now the equation of our line is: y = 5x + b

Let's plug one of our points into this equation to solve for b.

3 = 5(2) + b

3 = 10 + b

Subtract 10 from both sides.

-7 = b

The equation of our line is: y = 5x - 7

Slope [ y2-y1/x2-x1 ]

Slope-intercept form [ y = mx + b ]

-12-3/-1-2

-15/-3

5

y = 5x + b

3 = 5(2) + b

3 = 10 + b

3 - 10 = 10 - 10 + b

-7 = b

y = 5x - 7

Best of Luck!