Find the equation of a line that contains the points (−2,2) and (−6,−5). Write the equation in slope-intercept form, using fractions when required.

y = (4/7)X + 22/7

Step-by-step explanation:

Moving from (-2, 2) to (-6, -5), we see that x (the "run") decreases by 4 and y (the "rise") decreases by 7 (from 2 to -5).  Thus, the slope is m = rise / run =

-4/(- 7) = 4/7.  The slope intercept form y = mx + b takes on the specific values 4/7 for m, 2 for y and -2 for x:

2 = 4/7(-2) + b, or 14 = -8 + 7b.  Thus, 22 = 7b, and b = 22/7.

The desired equation is y = (4/7)X + 22/7.