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

Question

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

GPT-4o mini · Answer

Krystina is incorrect because she calculated the change in y over the change in x instead of the other way around. The formula for slope is given as:

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

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

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

Calculating the changes in y and x:

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

Now, substituting these values into the slope formula:

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

Thus, the correct slope is \(-\frac{5}{3}\), not \(-35\), indicating that Krystina's calculation and reasoning are flawed. The appropriate response would be:

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