Question

Which of the following equations describe the line (-6, 2) (-1, -4)? (Graph below)

A. y - 4 = -5/6(x - 1)
B. y - 2 = -5/6(x + 6)
C. y + 4 = -6/5(x + 1)
D. y + 4 = -5/6(x + 1)
E. y - 2 = -6/5(x + 6)
F. y - 6 = -6/5(x + 2)

Answer 1

I notice that all the choices are written in Point-Slope Formula. This is a key factor in answering your question. 

So usually we solve for slope, plug into point-slope form, then solve for slope intercept.

We only have to do the first 2 steps: 

Formula for slope: $\frac{y2-y1}{x2-x1}$
Plug in values: $\frac{-4-2}{-1-(-6)} = \frac{-6}{5}$
Slope: $- \frac{6}{5}$
Point-slope formula: $y - y1 = m(x-x1)$ where m is equivalent to slope. 
Plug in values: $y -2 = -\frac{6}{5}(x + 6)$ 


We can also rewrite the equation like this using the other coordinates. 

Plug in value: $y + 4 = - \frac{6}{5}(x + 1)$