Determine the intercepts of the line that correspond to the following table of values. x 2,6,10. y -18,-27,-36

x-int.:  (-6, 0); y-int.:  (0, -27/2).

Step-by-step explanation:

From this table of values we take two points:  (2, -18) and ( 6, -27).  Going from (2, -18) to (6, -27), we see that x increases by 4 and y decreases by 9.  Thus, the slope is m = rise / run = -9/4.

The equation of the line, in point-slope form, is then   y - (-18) = (-9/4)(x - 2).  Note that we don't ned (6, -27) again.  

This equation simplifies to y + 18 = (-9/4)(x - 2).

x-intercept:  Set y = 0 and find x:  0 + 18 = (-9/4)(x - 2).  To isolate (x - 2), mult. both sides of this equation by (-4/9):

(-4/9)(18) = (-4/9)(-9/4)(x - 2).  Then -8 = x - 2, or x = -6.  The x-intercept is then (-6, 0).

y-intercept:  Set x = 0 and find y:  y + 18 = (-9/4)(0 - 2).  This becomes

                                                        y = -18 + 9/2, or y = -27/2.  The y-intercept is thus (0, -27/2).