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 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.

Stephen is correct.

Answer 1

Let's break down Stephen's calculation of the slope using the formula for the slope of a line, which is:

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

In this case, we have the coordinates (8, -6) and (0, 8). We can label them as follows:

- Point 1: \((x_1, y_1) = (8, -6)\)
- Point 2: \((x_2, y_2) = (0, 8)\)

Now, let’s plug these values into the slope formula:

\[
\text{slope} = \frac{8 - (-6)}{0 - 8}
\]

Calculating the numerator:

\[
8 - (-6) = 8 + 6 = 14
\]

Calculating the denominator:

\[
0 - 8 = -8
\]

Now, putting it all together:

\[
\text{slope} = \frac{14}{-8} = -\frac{7}{4}
\]

Now we can see that Stephen's calculation of the slope was incorrect. He wrote \(0 - 8\) in the denominator but didn't process the changes in y and x correctly. He incorrectly cited \(0\) as being used in the formula and he mistakenly calculated the change in y (leading to the '−47').

Thus, the correct response is:

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