The graph of y=f(x) is shown in red below. Assuming the graph consists of three line segments, what is f(-2)?

The point  ( -2, f(-2) ) lies on the leftmost line segment.

The leftmost line segment contains the points  (-4, 4)  and  (-1, -1) .

So the slope of this line segment  =  [ -1 - 4 ] / [ -1 - -4 ]   =   -5 / 3  .

We know that the slope between  (-2, f(-2) )  and  (-1, -1)  will also be  -5/3 .

Using the slope  -5/3  and the points  (-1, -1)   and   (-2, f(-2) )

-5/3  =  [ f(-2) - -1 ] / [-2 - -1]

-5/3  =  [ f(-2) + 1 ] / [ -1 ]         Multiply both sides by  -1 .

5/3  =  f(-2) + 1                     Subtract  1  from both sides.

5/3 - 1  =  f(-2)

2/3  =  f(-2)

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