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 incorrect because he calculated the change in x over the change in y.
Stephen is incorrect because he calculated the change in x over the change in y.

Stephen is correct.
Stephen is correct.

Stephen is incorrect because he added instead of subtracted.

Answer 1

To determine if Stephen's calculation is correct, let's use the slope formula given by:

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

Given the points \((8, -6)\) as \((x_1, y_1)\) and \((0, 8)\) as \((x_2, y_2)\), we can identify:

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

Now, we substitute these values into the slope formula:

\[
m = \frac{8 - (-6)}{0 - 8} = \frac{8 + 6}{0 - 8} = \frac{14}{-8} = -\frac{14}{8} = -\frac{7}{4}
\]

Now checking Stephen's calculation, he used:

\[
0 - 8 \quad \text{and} \quad -6
\]

He mistakenly computed it as:

\[
0 - 8 = -8 \quad \text{and} \quad 8 - (-6) = 8 + 6 = 14
\]

Therefore, his calculation seemed to be mixed up.

Based on the right computation, we see that Stephen's interpretation and calculation is indeed incorrect.

The correct answer is:

**Stephen is incorrect because he calculated the change in x over the change in y.**