Question

Krystina is trying to derive the slope of a line with coordinates (6,−2) and (0,8) using the formula ΔyΔx=y2−y1x2−x1 . Krystina says the slope is −35 because slope =riserun=x2−x1y2−y1=0−68−(−2)=−68+2=−610 . Is Krystina’s calculation for slope correct? If not, what is an appropriate explanation for why she is incorrect? (1 point) Responses Krystina is correct and she simplified the slope correctly. Krystina is correct and she simplified the slope correctly. Krystina is correct because she calculated the change in x over the change in y. Krystina is correct because she calculated the change in x over the change in y. Krystina is incorrect because she calculated the change in x over the change in y. Krystina is incorrect because she calculated the change in x over the change in y. Krystina is incorrect because she calculated the change in y over the change in x.

Answer 1

Krystina is incorrect because she calculated the change in y over the change in x instead of the correct way, which is change in y over change in x.

To find the slope \( m \) of the line that passes through the points \((6, -2)\) and \((0, 8)\), you should use the formula:

\[
m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Assign the coordinates:
- \((x_1, y_1) = (6, -2)\)
- \((x_2, y_2) = (0, 8)\)

Now plug in the values:

\[
m = \frac{8 - (-2)}{0 - 6} = \frac{8 + 2}{0 - 6} = \frac{10}{-6} = -\frac{5}{3}
\]

Thus, the correct slope is \(-\frac{5}{3}\), not \(-35\). Krystina's statement shows she incorrectly calculated using the changes in x and y.