Kevin's calculation involves finding the rate of change or slope of a function between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]. The general formula for the slope between two points is:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Kevin performed the calculation as follows:
[tex]\[
\frac{4 - 0}{0 - 2} = \frac{4}{-2} = -2
\][/tex]
Let's break down the steps:
1. Kevin identified the points on the graph correctly as [tex]\((x_2, y_2) = (0, 4)\)[/tex] and [tex]\((x_1, y_1) = (2, 0)\)[/tex].
2. He used these points in the slope formula: [tex]\(\frac{y_2 - y_1}{x_2 - x_1}\)[/tex].
3. Substituting the coordinates into the formula:
[tex]\[
\frac{4 - 0}{0 - 2}
\][/tex]
Here, Kevin calculated the numerator correctly as [tex]\(4 - 0 = 4\)[/tex], but there is an error in the denominator calculation. The correct calculation should be:
[tex]\[
0 - 2 = -2
\][/tex]
However, Kevin’s mistake is stated as: "He subtracted -2 from 0 when he should have added -2 to 0."
This indicates that Kevin might have misinterpreted the operation in the denominator. Instead of correctly performing [tex]\(0 - 2\)[/tex], he incorrectly might have approached it as subtracting [tex]\(-2\)[/tex] (as though he had an expression like [tex]\(0 - (-2)\)[/tex]), which should indeed be [tex]\(0 + 2 = 2\)[/tex].
In summary, Kevin's mistake was he subtracted -2 from 0 when he should have added -2 to 0.
