Question

Find the set of points with the slope of –1 that passes through them.

(0, 4), (4, 0)

(2, –4), (–2, 4)

(0, 4), (0, 0)

(4, 0), (0, 0)

(2, 10), (10, 6)

Answer 1

To determine which pairs of points have a slope of -1, we can use the slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

We will calculate the slope for each pair of points.

1. **Points (0, 4) and (4, 0)**:
\[
\text{slope} = \frac{0 - 4}{4 - 0} = \frac{-4}{4} = -1
\]

2. **Points (2, -4) and (-2, 4)**:
\[
\text{slope} = \frac{4 - (-4)}{-2 - 2} = \frac{4 + 4}{-4} = \frac{8}{-4} = -2
\]

3. **Points (0, 4) and (0, 0)**:
\[\text{Slope is undefined (vertical line)}\]

4. **Points (4, 0) and (0, 0)**:
\[
\text{slope} = \frac{0 - 0}{0 - 4} = \frac{0}{-4} = 0
\]

5. **Points (2, 10) and (10, 6)**:
\[
\text{slope} = \frac{6 - 10}{10 - 2} = \frac{-4}{8} = -\frac{1}{2}
\]

After analyzing all the pairs, we find that the only pair of points that has a slope of -1 is **(0, 4) and (4, 0)**.