Answer:
15x + 14y + 36 = 0
Explanation:
As we travel from the point (-8, 6) to the point (6, - 9), the increase in x (the "run") is 14 and that in y (the "rise") is -15. Thus, the slope of the line segment connecting these two points is m = rise / run = -15 / 14.
Let's use the point (6, -9) and the slope m = -15/14 to write the equation of this line:
Adapting y = mx + b, we get:
-9 = (-15/14)(6) + b, or
-9 = -45/7 + b, which yields b = 45/7 - 9, or b = 45/7 - 63/7, or b = -18/7
Then the equation is y = (-15/14)x - 18/7
We must put this into "standard form." Multiplying all three terms by 14 to clear the fractions out, we get:
14y = -15x - 36, or (in standard form):
15x + 14y + 36 = 0