Payton is trying to derive the slop of a line with the coordinates (6, -2) and (0,8) using the formula △y/△x = y2-y1/ x2-x1. Payton says the slope is -3/5 because slope = rise/run = y2-y1/ x2-x1 = 0-6/8-(-2) = -6/8+2 = -6/10. Is Payton's calculation for slope correct? If not, what is an appropriate explanation for why she is correct?

Question

a. Payton is incorrect because she calculated the change in x over the change in y
b. Payton is incorrect because she calculated the change in y over the change in x
c. Payton is correct because she calculated the change in x over the change in y
d. Payton is correct, and she is simplified the slope correctly.

Answer 1

Payton's calculation for the slope is incorrect. The formula for slope \( m \) is given by:

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

For the coordinates (6, -2) and (0, 8):

• Let \( (x_1, y_1) = (6, -2) \) and \( (x_2, y_2) = (0, 8) \).

Using the formula:

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

Now, analyzing Payton's calculation:

• She incorrectly used \( y_2 - y_1 \) as \( 0 - 6 \) instead of \( 8 - (-2) \).
• She also miscalculated \( x_2 - x_1 \) as \( 8 - (-2) \), leading to confusion in the values.

Given this, the correct answer is:

b. Payton is incorrect because she calculated the change in y over the change in x.