Krystina is trying to derive the slope of a line with coordinates (6,−2) and (0,8) using the formula ΔyΔx=y2−y1x2−x1.

Question

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 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 because she calculated the change in x over the change in y.

To find the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\), the formula is:

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

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

• Let \((x_1, y_1) = (6, -2)\) and \((x_2, y_2) = (0, 8)\).
• So, \(y_2 - y_1 = 8 - (-2) = 8 + 2 = 10\).
• And \(x_2 - x_1 = 0 - 6 = -6\).

Thus, the slope is:

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

Krystina's errors lie in both substituting the coordinates incorrectly and also in her arithmetic. She miscalculated the change in both x and y values, leading to her incorrect slope result of -35.