Question

Determine the equation of a line, in slope-intercept form, that passes through the points (9, -2) and (12, 0).

Answer 1

As x increases from 9 to 12 (a change of 3), y increases from -2 to 0 (a change of 2).  Thus, the slope of this line is 2/3.

Subbing this info and the coordinates of one of the points into y = mx + b, we get:

-2 = (2/3)(9) + b.  Solving for b:  b = -2 -18/3 = -8.  Then the equation of this line is:

y = (2/3)x - 8.

Check by subst.:  Does (12,0) satisfy this equation?  0 = (2/3)(12) - 8?  Yes.