To determine which ordered pairs could be points on a parallel line with a slope of [tex]\(-\frac{3}{5}\)[/tex], we need to verify the slope calculated between the points in each pair. 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]
We will calculate the slope for each pair of points and determine if it matches the given slope of [tex]\(-\frac{3}{5}\)[/tex].
### Pair 1: [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]
Calculate the slope:
[tex]\[
m = \frac{2 - 8}{2 - (-8)} = \frac{2 - 8}{2 + 8} = \frac{-6}{10} = -\frac{3}{5}
\][/tex]
This pair matches the slope of [tex]\(-\frac{3}{5}\)[/tex].
### Pair 2: [tex]\((-5, -1)\)[/tex] and [tex]\((0, 2)\)[/tex]
Calculate the slope:
[tex]\[
m = \frac{2 - (-1)}{0 - (-5)} = \frac{2 + 1}{0 + 5} = \frac{3}{5}
\][/tex]
This pair does not match the slope of [tex]\(-\frac{3}{5}\)[/tex].
### Pair 3: [tex]\((-3, 6)\)[/tex] and [tex]\((6, -9)\)[/tex]
Calculate the slope:
[tex]\[
m = \frac{-9 - 6}{6 - (-3)} = \frac{-9 - 6}{6 + 3} = \frac{-15}{9} = -\frac{5}{3}
\][/tex]
This pair does not match the slope of [tex]\(-\frac{3}{5}\)[/tex].
### Pair 4: [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]
Calculate the slope:
[tex]\[
m = \frac{-2 - 1}{3 - (-2)} = \frac{-2 - 1}{3 + 2} = \frac{-3}{5} = -\frac{3}{5}
\][/tex]
This pair matches the slope of [tex]\(-\frac{3}{5}\)[/tex].
### Pair 5: [tex]\((0, 2)\)[/tex] and [tex]\((5, 5)\)[/tex]
Calculate the slope:
[tex]\[
m = \frac{5 - 2}{5 - 0} = \frac{5 - 2}{5} = \frac{3}{5}
\][/tex]
This pair does not match the slope of [tex]\(-\frac{3}{5}\)[/tex].
Given the calculations, the pairs of points that have a slope of [tex]\(-\frac{3}{5}\)[/tex] and thus could lie on a line parallel to the given line are:
1. [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]
2. [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]
