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

Question

GPT-4o mini · Answer

Krystina is incorrect because she calculated the change in y over the change in x incorrectly. The slope formula is given by:

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

With her points (6, −2) and (0, 8), we assign:

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

Now calculating:

\[ \Delta y = y_2 - y_1 = 8 - (-2) = 8 + 2 = 10 \] \[ \Delta x = x_2 - x_1 = 0 - 6 = -6 \]

Now plugging these values into the slope formula:

\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{10}{-6} = -\frac{5}{3} \]

Thus, Krystina's calculation is incorrect, and she made errors in both the subtraction and in her interpretation of the points. The correct slope is \(-\frac{5}{3}\).