Question

Stephen is trying to find the slope of a line that goes through the coordinates (8,-6) and (0,8) using the formula ΔyΔx=y2−y1x2−x1 . Stephen says the slope should be calculated as 0−88−(−6) = −47 . Is his calculation for slope correct? If not, why?(1 point) Responses Stephen is incorrect because he didn't simplify correctly. Stephen is incorrect because he didn't simplify correctly. Stephen is correct. Stephen is correct. Stephen is incorrect because he added instead of subtracted. Stephen is incorrect because he added instead of subtracted. Stephen is incorrect because he calculated the change in x over the change in y.

Answer 1

Stephen's calculation for slope is incorrect. The correct formula for the slope (m) is given by:

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

In this case, we can identify the points as follows:

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

Now, substituting the values into the slope formula:

1. Calculate \( \Delta y \): \[ y_2 - y_1 = 8 - (-6) = 8 + 6 = 14 \]

2. Calculate \( \Delta x \): \[ x_2 - x_1 = 0 - 8 = -8 \]

Now, we can compute the slope: \[ m = \frac{14}{-8} = -\frac{7}{4} \]

From this calculation, we conclude that Stephen's error comes from using incorrect values and the wrong steps in his calculation. Thus, the correct statement would be:

Stephen is incorrect because he added instead of subtracted.