To determine if Stephen's calculation is correct, let's use the slope formula given by:
\[ \text{slope} (m) = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Given the points \((8, -6)\) as \((x_1, y_1)\) and \((0, 8)\) as \((x_2, y_2)\), we can identify:
- \(x_1 = 8\)
- \(y_1 = -6\)
- \(x_2 = 0\)
- \(y_2 = 8\)
Now, we substitute these values into the slope formula:
\[ m = \frac{8 - (-6)}{0 - 8} = \frac{8 + 6}{0 - 8} = \frac{14}{-8} = -\frac{14}{8} = -\frac{7}{4} \]
Now checking Stephen's calculation, he used:
\[ 0 - 8 \quad \text{and} \quad -6 \]
He mistakenly computed it as:
\[ 0 - 8 = -8 \quad \text{and} \quad 8 - (-6) = 8 + 6 = 14 \]
Therefore, his calculation seemed to be mixed up.
Based on the right computation, we see that Stephen's interpretation and calculation is indeed incorrect.
The correct answer is:
Stephen is incorrect because he calculated the change in x over the change in y.