Find the slope of the line passing through the points (a, -6a + 5) and (a + h, -6(a-9h)+5).?

Answer 1

Slope is defined as the rise over the run, or the difference of the y coordinates divided by the difference of the x coordinates.

Point 1: (a, -6a + 5)
Point 2: (a + h, -6(a - 9h) + 5)

Difference of y coordinates (y2 - y1):
-6(a - 9h) + 5 - (-6a + 5)
= -6a + 54h + 5 +6a - 5
= 54h

Difference of x coordinates (x2 - x1):
a + h - a
= h

So the slope is:
54h / h
= 54

The slope is 54

(Isn't it nice how everything canceled out?)

Answer 2

(a, b) and (c, d)

(b - d) / (a - c) = slope

Substitute what you have into this equation.