Connect with a knowledgeable community and get your questions answered on IDNLearn.com. Get the information you need from our community of experts, who provide detailed and trustworthy answers.
Sagot :
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]
[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]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.