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 . Payton says the slope is −35 because slope = riserun = 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. 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 formula for slope (m) is given by:

$$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{y_2-y_1}{x_2-x_1}$$

Given the points (6, -2) and (0, 8), we can assign:

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

Now we can find $\mathrm{\Delta }y$ and $\mathrm{\Delta }x$:

$$\mathrm{\Delta }y=y_2-y_1=8-(-2)=8+2=10$$

$$\mathrm{\Delta }x=x_2-x_1=0-6=-6$$

Now substitute these values into the slope formula:

$$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{10}{-6}=-\frac{5}{3}$$

Therefore, Payton is incorrect because she calculated the change in $y$ (rise) over the change in $x$ (run), but she made mistakes in her arithmetic.

So the most appropriate explanation is: Payton is incorrect because she calculated the change in $y$ over the change in $x$.