Question

A line has a slope of Negative three-fifths. Which ordered pairs could be points on a parallel line? Select two options.

(–8, 8) and (2, 2)
(–5, –1) and (0, 2)
(–3, 6) and (6, –9)
(–2, 1) and (3, –2)
(0, 2) and (5, 5)

Answer 1

To determine which ordered pairs could be points on a parallel line to the one with a slope of \(-\frac{3}{5}\), we need to look for points that also yield the same slope when calculating the slope between the two points in each pair.

The formula for calculating the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Now, we'll calculate the slope for each pair of points provided:

1. **For (–8, 8) and (2, 2)**:
\[
m = \frac{2 - 8}{2 - (-8)} = \frac{-6}{10} = -\frac{3}{5}
\]

2. **For (–5, –1) and (0, 2)**:
\[
m = \frac{2 - (-1)}{0 - (-5)} = \frac{3}{5}
\]

3. **For (–3, 6) and (6, –9)**:
\[
m = \frac{-9 - 6}{6 - (-3)} = \frac{-15}{9} = -\frac{5}{3}
\]

4. **For (–2, 1) and (3, –2)**:
\[
m = \frac{-2 - 1}{3 - (-2)} = \frac{-3}{5}
\]

5. **For (0, 2) and (5, 5)**:
\[
m = \frac{5 - 2}{5 - 0} = \frac{3}{5}
\]

Now we can summarize the results:

- The slope for points **(–8, 8) and (2, 2)** is \(-\frac{3}{5}\).
- The slope for points **(–5, –1) and (0, 2)** is \(\frac{3}{5}\).
- The slope for points **(–3, 6) and (6, –9)** is \(-\frac{5}{3}\).
- The slope for points **(–2, 1) and (3, –2)** is \(-\frac{3}{5}\).
- The slope for points **(0, 2) and (5, 5)** is \(\frac{3}{5}\).

Thus, the pairs of points that could be on a parallel line (having the same slope of \(-\frac{3}{5}\)) are:

- (–8, 8) and (2, 2)
- (–2, 1) and (3, –2)

So the answer is:

- (–8, 8) and (2, 2)
- (–2, 1) and (3, –2)