I'll need to assume that your "-14,9" means (-14,9); if so, please use parentheses next time to indicate that you're sharing the coordinates of a point.
As we go from (-14,9) to (-10,18), x increases by 4 and y increases by 9. Thus, the slope of this line is m = rise / run = 9/4.
We want the intercepts of this line. Let's use the slope-intercept form y = mx + b. Substituting the given info: -10 for x and 18 for y, and m = 9/4, we get:
18 = (9/4)(-10) + b, where b is the y-intercept.
Solving for b, we get 18 + 90/4 = (72+90)/4 = 162/4, or 81/2.
Then b = 81/2, and the equation of the line is y = (9/4)x + 81/2.
Now find the x-intercept. To do this, let y = 0; then (9/4)x = -81/2, Mult. both sides by 4 to eliminate the fractions: 9x = -162, or x = -18. The x-intercept is (-18,0) and the y-intercept is (0,81/2)