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 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 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 y over the change in x. Krystina is incorrect because she calculated the change in y over the change in x. Krystina is correct and she simplified the slope correctly.

Answer 1

Krystina is incorrect because she calculated the change in y over the change in x. The correct formula for the slope (m) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points (6, −2) and (0, 8):

- \(y_1 = -2\)
- \(y_2 = 8\)
- \(x_1 = 6\)
- \(x_2 = 0\)

Plugging these values into the formula gives us:

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

Thus, the slope is \(-\frac{5}{3}\), not \(-35\) as Krystina claimed.