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 −3/5 because slope =rise/run=x2−x1/y2−y1=0−6/8−(−2)=−6/8+2=−6/10 . Is Krystina’s calculation for slope correct? If not, what is an appropriate explanation for why she is incorrect?

Question

A. Krystina is correct and she simplified the slope correctly.
B. Krystina is incorrect because she calculated the change in x over the change in y.
C. Krystina is correct because she calculated the change in x over the change in y.
D. Krystina is incorrect because she calculated the change in y over the change in x.

Answer 1

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

To clarify, the slope formula is given by \(\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}\). For the points (6, -2) and (0, 8):

• Let (x1, y1) = (6, -2)
• Let (x2, y2) = (0, 8)

Now, calculating the changes:

• \(y_2 - y_1 = 8 - (-2) = 8 + 2 = 10\)
• \(x_2 - x_1 = 0 - 6 = -6\)

Putting these into the formula yields:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10}{-6} = -\frac{5}{3} \]

Krystina mistakenly calculated the changes in x and y incorrectly and thus arrived at an incorrect slope of \(-\frac{3}{5}\). Therefore, the appropriate explanation is D.