Answer:
x-intercept: (-21,0); y-intercept: (0, 14)
Explanation:
Let's first look at changes in x. x begins at -24 and increases by 9 to -15. At the same time, y begins at -2 and decreases to -8. Thus, the slope of the line in question is m = rise / run = -6/9 = -2/3.
Let's find the equation of the line in the simplest way: point-slope form.
y-(-2) = (-2/3)(x-[-24]). Then y+2 = (-2/3)x - (2/3)(24)), or
y + 2 = - (2/3)x + 16.
x-intercept: Let y = 0 and find x: 0 + 2 = -(2/3)x + 16, or 0 = -(2/3)x + 14.
Multiplying all terms by (-3/2), we get 0 = -x + 14(-3/2), or x = -21. Then the x-intercept is (-21, 0).
y-intercept: let x = 0 and find y: y + 2 = -(2/3)(0) + 16. Then y = 14. The y-intercept is (0, 14).