To determine which ordered pairs could be points on a line that is parallel to a given line with a slope of [tex]\(-\frac{3}{5}\)[/tex], we need to calculate the slopes between each pair of given points and compare them with [tex]\(-\frac{3}{5}\)[/tex].
1. Points: [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]
- The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
- Substituting the given points:
[tex]\[
m = \frac{2 - 8}{2 - (-8)} = \frac{-6}{10} = -\frac{3}{5}
\][/tex]
- The slope is [tex]\(-\frac{3}{5}\)[/tex], which matches the given slope.
2. Points: [tex]\((-5, -1)\)[/tex] and [tex]\((0, 2)\)[/tex]
- Substituting the given points:
[tex]\[
m = \frac{2 - (-1)}{0 - (-5)} = \frac{3}{5}
\][/tex]
- The slope is [tex]\(\frac{3}{5}\)[/tex], which does not match the given slope.
3. Points: [tex]\((-3, 6)\)[/tex] and [tex]\((6, -9)\)[/tex]
- Substituting the given points:
[tex]\[
m = \frac{-9 - 6}{6 - (-3)} = \frac{-15}{9} = -\frac{5}{3}
\][/tex]
- The slope is [tex]\(-\frac{5}{3}\)[/tex], which does not match the given slope.
4. Points: [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]
- Substituting the given points:
[tex]\[
m = \frac{-2 - 1}{3 - (-2)} = \frac{-3}{5}
\][/tex]
- The slope is [tex]\(-\frac{3}{5}\)[/tex], which matches the given slope.
5. Points: [tex]\((0, 2)\)[/tex] and [tex]\((5, 5)\)[/tex]
- Substituting the given points:
[tex]\[
m = \frac{5 - 2}{5 - 0} = \frac{3}{5}
\][/tex]
- The slope is [tex]\(\frac{3}{5}\)[/tex], which does not match the given slope.
Thus, the ordered pairs that could be points on a line parallel to the given line with a slope of [tex]\(-\frac{3}{5}\)[/tex] are:
[tex]\[
(-8,8) \text{ and } (2,2)
\][/tex]
[tex]\[
(-2,1) \text{ and } (3,-2)
\][/tex]
