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 x over the change in y.
Krystina is incorrect 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 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 correct and she simplified the slope correctly.

Answer 1

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

To find the slope (m) using the formula \( m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \), you should subtract the y-coordinates of the two points and the x-coordinates of the two points in the appropriate order.

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

• \( y_2 = 8 \), \( y_1 = -2 \), so \( \Delta y = 8 - (-2) = 8 + 2 = 10 \)
• \( x_2 = 0 \), \( x_1 = 6 \), so \( \Delta x = 0 - 6 = -6 \)

Therefore, the slope is: \[ m = \frac{10}{-6} = -\frac{5}{3} \]

Krystina's calculations were incorrect, leading her to an incorrect slope value.