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?

Question

Possible Answers:
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 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.

Answer 1

Krystina is incorrect in her calculation of the slope. The correct formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

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

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

Now, we plug these values into the slope formula:

\[ m = \frac{8 - (-2)}{0 - 6} = \frac{8 + 2}{0 - 6} = \frac{10}{-6} = -\frac{5}{3} \]

Krystina's calculation leads her to an incorrect slope of -35. The main error in her reasoning is that she calculated the change in \(y\) correctly, but she appears to have misunderstood the order or values for \(x_2\) and \(x_1\) in her denominator. This confusion caused her to miscalculate the change in \(x\).

So the correct answer is:

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