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 . Payton says the slope is −35 because slope = rise run = y2 −y1x2−x1 = 0−68−(−2) = −68+2 = −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 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 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 x over the change in y.

Question

GPT-4o mini · Answer

Payton's calculation for the slope is incorrect.

The formula for the slope \( m \) of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

In this case, the points are \((6, -2)\) and \((0, 8)\). We can assign:

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

Now, substituting into the formula:

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

Payton incorrectly mixed up the order of the coordinates and ended up calculating the slope as \(-35\) when, in fact, the correct slope is \(-\frac{5}{3}\). Therefore, the appropriate explanation is that Payton is incorrect because she calculated the change in \(y\) over the change in \(x\) incorrectly, and she did not use the correct coordinates properly in her formula.