5 4 3 2 1
1 2
3 4 5 x
Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the
graph to be (-1,-4), (0, -3), and (2,5). Next, she determined the rate of change between the points (-1, 4) and (0, -3) to
-3-(-4) 1
5-(-3) 8
be 0-(-1) - 7and the rate of change between the points (0, -3) and (2,5) to be 2-0^-5 = 4 Finally, she
concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?
The points (-1,-4), (0, -3), and (2,5) are not all on the graph.
-3-(-4) -3-(-5)
The expressions 0-(-1) and 2-0 both equal 1.
She miscalculated the rates of change.
Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.