Determine the intercepts of the line that correspond to the following table of values

x-intercept:  (-21,0); y-intercept:  (0, 14)

Step-by-step 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).