Question

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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.

Answer 1

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

To calculate the slope correctly, we should use the formula \( \text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \).

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

1. Let \( (x_1, y_1) = (6, -2) \) and \( (x_2, y_2) = (0, 8) \).
2. Calculate \( \Delta y = y_2 - y_1 = 8 - (-2) = 8 + 2 = 10 \).
3. Calculate \( \Delta x = x_2 - x_1 = 0 - 6 = -6 \).

Now, substitute these values into the slope formula:

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

Thus, the correct slope is \(-\frac{5}{3}\).