A line has a slope of [tex]\(-\frac{3}{5}\)[/tex]. Which ordered pairs could be points on a parallel line? Select two options.

A. [tex]\((-8,8)\)[/tex] and [tex]\((2,2)\)[/tex]

B. [tex]\((-5,-1)\)[/tex] and [tex]\((0,2)\)[/tex]

C. [tex]\((-3,6)\)[/tex] and [tex]\((6,-9)\)[/tex]

D. [tex]\((-2,1)\)[/tex] and [tex]\((3,-2)\)[/tex]

E. [tex]\((0,2)\)[/tex] and [tex]\((5,5)\)[/tex]



Answer :

To determine which ordered pairs could be points on a line parallel to a given line with a slope of [tex]\(-\frac{3}{5}\)[/tex], we need to identify pairs of points that yield the same slope when a line is drawn through them.

For each pair of points, we will calculate the slope using the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Let's analyze each pair:

1. For the points [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]:
[tex]\[ m = \frac{2 - 8}{2 - (-8)} = \frac{-6}{10} = -\frac{3}{5} \][/tex]
This pair has a slope of [tex]\(-\frac{3}{5}\)[/tex], which matches the given slope.

2. For the points [tex]\((-5, -1)\)[/tex] and [tex]\((0, 2)\)[/tex]:
[tex]\[ m = \frac{2 - (-1)}{0 - (-5)} = \frac{3}{5} \][/tex]
This pair has a slope of [tex]\(\frac{3}{5}\)[/tex], which does not match the given slope.

3. For the points [tex]\((-3, 6)\)[/tex] and [tex]\((6, -9)\)[/tex]:
[tex]\[ m = \frac{-9 - 6}{6 - (-3)} = \frac{-15}{9} = -\frac{5}{3} \][/tex]
This pair has a slope of [tex]\(-\frac{5}{3}\)[/tex], which does not match the given slope.

4. For the points [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]:
[tex]\[ m = \frac{-2 - 1}{3 - (-2)} = \frac{-3}{5} = -\frac{3}{5} \][/tex]
This pair has a slope of [tex]\(-\frac{3}{5}\)[/tex], which matches the given slope.

5. For the points [tex]\((0, 2)\)[/tex] and [tex]\((5, 5)\)[/tex]:
[tex]\[ m = \frac{5 - 2}{5 - 0} = \frac{3}{5} \][/tex]
This pair has a slope of [tex]\(\frac{3}{5}\)[/tex], which does not match the given slope.

After analyzing each pair, the pairs whose slopes match the given slope of [tex]\(-\frac{3}{5}\)[/tex] are:

1. [tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex]
2. [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex]

Therefore, the two options that could be points on a parallel line are:
[tex]\((-8, 8)\)[/tex] and [tex]\((2, 2)\)[/tex], as well as [tex]\((-2, 1)\)[/tex] and [tex]\((3, -2)\)[/tex].