To determine which ordered pairs could be points on a line parallel to one with a slope of [tex]\(-\frac{3}{5}\)[/tex], we need to calculate the slope between each pair of points given and check whether they match the original slope.
Recall that the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's go through each pair of points step by step:
1. Points [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]:
[tex]\[
m = \frac{2 - 8}{2 - (-8)} = \frac{2 - 8}{2 + 8} = \frac{-6}{10} = -\frac{3}{5}
\][/tex]
The slope here is [tex]\(-\frac{3}{5}\)[/tex], which matches the original slope.
2. Points [tex]\((-5, -1)\)[/tex] and [tex]\((0, 2)\)[/tex]:
[tex]\[
m = \frac{2 - (-1)}{0 - (-5)} = \frac{2 + 1}{0 + 5} = \frac{3}{5}
\][/tex]
The slope here is [tex]\(\frac{3}{5}\)[/tex], which does not match the original slope of [tex]\(-\frac{3}{5}\)[/tex].
3. Points [tex]\((-3, 6)\)[/tex] and [tex]\((6, -9)\)[/tex]:
[tex]\[
m = \frac{-9 - 6}{6 - (-3)} = \frac{-9 - 6}{6 + 3} = \frac{-15}{9} = -\frac{5}{3}
\][/tex]
The slope here is [tex]\(-\frac{5}{3}\)[/tex], which does not match the original slope.
4. Points [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]:
[tex]\[
m = \frac{-2 - 1}{3 - (-2)} = \frac{-2 - 1}{3 + 2} = \frac{-3}{5}
\][/tex]
The slope here is [tex]\(-\frac{3}{5}\)[/tex], which matches the original slope.
5. Points [tex]\((0, 2)\)[/tex] and [tex]\((5, 5)\)[/tex]:
[tex]\[
m = \frac{5 - 2}{5 - 0} = \frac{3}{5}
\][/tex]
The slope here is [tex]\(\frac{3}{5}\)[/tex], which does not match the original slope.
From the calculations, the ordered pairs that have a slope of [tex]\(-\frac{3}{5}\)[/tex] and thus are parallel to the given line are:
- [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]
- [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]
Therefore, the correct options are:
- [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]
- [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]
