Krystina is incorrect because she calculated the change in y over the change in x instead of the other way around. The formula for slope is given as:
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points (6, -2) and (0, 8):
- \(x_1 = 6\), \(y_1 = -2\)
- \(x_2 = 0\), \(y_2 = 8\)
Calculating the changes in y and x:
\[ \Delta y = y_2 - y_1 = 8 - (-2) = 8 + 2 = 10 \] \[ \Delta x = x_2 - x_1 = 0 - 6 = -6 \]
Now, substituting these values into the slope formula:
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{10}{-6} = -\frac{5}{3} \]
Thus, the correct slope is \(-\frac{5}{3}\), not \(-35\), indicating that Krystina's calculation and reasoning are flawed. The appropriate response would be:
Krystina is incorrect because she calculated the change in y over the change in x.