To determine if Stephen's calculation for the slope is correct, let's use the formula for the slope, which is given by:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the coordinates (8, -6) as \((x_1, y_1)\) and (0, 8) as \((x_2, y_2)\):
- \(x_1 = 8\)
- \(y_1 = -6\)
- \(x_2 = 0\)
- \(y_2 = 8\)
Now, substituting these values into the slope formula:
\[ m = \frac{8 - (-6)}{0 - 8} = \frac{8 + 6}{0 - 8} = \frac{14}{-8} = -\frac{7}{4} \]
Stephen's calculation was incorrect, as he stated the slope to be \(-47\) and did not properly calculate the differences.
The correct reason for Stephen's incorrect answer is that he miscalculated the changes in y and x (adding instead of subtracting). Thus, the appropriate response is:
Stephen is incorrect because he added instead of subtracted.