Question

Krystina is trying to derive the slope of a line with coordinates (6,−2)
and (0,8)
using the formula ΔyΔx=y2−y1x2−x1
.

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 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 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 correct and she simplified the slope correctly.
Krystina is correct and she simplified the slope correctly.

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

Answer 1

Krystina's calculation for the slope is incorrect.

The correct formula for the slope of a line is given by:

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

Let's define the points:
- Point 1: (6, -2) → \( (x_1, y_1) = (6, -2) \)
- Point 2: (0, 8) → \( (x_2, y_2) = (0, 8) \)

Now, calculating the slope:

\[
\Delta y = y_2 - y_1 = 8 - (-2) = 8 + 2 = 10
\]

\[
\Delta x = x_2 - x_1 = 0 - 6 = -6
\]

Now, plug these values into the slope formula:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{10}{-6} = -\frac{5}{3}
\]

In Krystina's calculation, she mistakenly calculated the changes and arrived at an incorrect result of \(-\frac{610}{10}\), which leads to a wrong value for the slope.

The correct response is:

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