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 correct and she simplified the slope correctly. Krystina is correct and she simplified the slope correctly. 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.

Question

GPT-4o mini · Answer

Krystina is incorrect because she calculated the change in $ x $ over the change in $ y $ instead of the correct way, which is the change in $ y $ over the change in $ x $.

The formula for slope $ m $ is:

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

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

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

Now, using the formula:

\[ \Delta y = y_2 - y_1 = -2 - 8 = -10 \] \[ \Delta x = x_2 - x_1 = 6 - 0 = 6 \] \[ m = \frac{\Delta y}{\Delta x} = \frac{-10}{6} = -\frac{5}{3} \]

Therefore, her statement that the slope is $ -35 $ is incorrect. The correct slope is $ -\frac{5}{3} $.

Answer

so what answer would it be?

GPT-4o mini · Answer

The correct answer is: **Krystina is incorrect because she calculated the change in $ y $ over the change in $ x $.** Her calculation for the slope was incorrect, and the correct calculation should be $ m = -\frac{5}{3} $.