Question

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

Answer 1

Let's first evaluate Stephen's calculation:

The formula for the slope (m) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Using the coordinates provided, \((8, -6)\) and \((0, 8)\), we can assign:

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

Substituting these values into the slope formula:

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

Now, let's analyze Stephen's claim:

Stephen computed the slope as \(0 - 8\) over \(8 - (-6)\), which is incorrect because he switched the coordinates and also simplified incorrectly:

- He used \(y_2 = 0\) and \(y_1 = 8\) mistakenly instead of \(y_2 = 8\) and \(y_1 = -6\).
- He also calculated \(x_1\) and \(x_2\) backwards.

Therefore, the correct answer would be:

**Stephen is incorrect because he added instead of subtracted.**