Question

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

Answer 1

Payton's calculation for the slope is incorrect. The correct formula for the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

In this case, the points are \((6, -2)\) and \((0, 8)\), so we can assign:
- \( (x_1, y_1) = (6, -2) \)
- \( (x_2, y_2) = (0, 8) \)

Using the formula, we compute the slope as follows:

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

Thus, Payton made an error in her calculation. Specifically, she calculated the change in \( y \) but called it change in \( x \) in her explanation. So the correct answer is:

Payton is incorrect because she calculated the change in \( y \) over the change in \( x \).