Determine the intercepts of the line that corresponds to the following table of values.

y-intercept is (0,30); x-intercept is (52.5,0).

Step-by-step explanation:

Note that as x increases by 7 from -35 to -28,   y decreases by 4 from 18 to 14.  Thus, the slope of this line is

m = rise / run = -4/7.

Let's find the equation of the line.  Start with the slope-intercept form:

y = mx + b.  Use the slope m = -4/7 and the point (-28, 14) to find b:

14 = -(4/7)(28) + b, or

14 = -16 + b.  Then b = 30, and the equation of the line in slope-intercept form is y = (-4/7)x + 30.  The y-intercept is (0, 30).

Find the x-intercept by setting y=0 and solving the resulting equation for x:

y = (-4/7)x + 30 becomes (4/7)x = 30, and x = (7/4)(30) = 214, or 52.5.

The x-intercept is thus (52.5, 0).