Kevin found the rate of change of the linear function graphed below.

Question

To find the rate of change, Kevin did the following:

4−00−2

=4−2

=−2

What was Kevin's mistake?

(1 point)
Responses

He subtracted -2 from 0 when he should have added -2 and 0.
He subtracted -2 from 0 when he should have added -2 and 0.

He incorrectly chose (4, 0) as a point on the graph.
He incorrectly chose (4, 0) as a point on the graph.

He incorrectly chose (0, 2) as a point on the graph.
He incorrectly chose (0, 2) as a point on the graph.

He mixed up the numerator and the denominator of the fraction.
He mixed up the numerator and the denominator of the fraction.

Answer 1

To find the rate of change of a linear function, Kevin should use the formula for the slope, which is:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

From what he wrote, it seems like he is trying to find the slope using points on the graph. The points he appears to be using are (0, 2) and (4, 0). By substituting these points into the slope formula, we have:

• \( (x_1, y_1) = (0, 2) \)
• \( (x_2, y_2) = (4, 0) \)

Plugging these into the slope formula gives:

\[ \text{slope} = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2} \]

Kevin, however, wrote:

\[ 4 - 0 - 2 = 4 - 2 = -2 \]

This suggests that Kevin made an error in how he structured his calculation of the change in the values. The correct numerator should have been \(0 - 2\) (the difference in y-values), rather than \(4 - 0\).

The appropriate option that describes Kevin’s mistake is: He mixed up the numerator and the denominator of the fraction.