we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
If two lines are parallel, then their slopes are equal
in this problem we have
the slope of the given line is [tex]m=-\frac{3}{5}[/tex]
if ordered pairs could be points on a parallel line, then the ordered pairs must have a slope equal to [tex]m=-\frac{3}{5}[/tex]
we are going to calculate the slope in each of the cases
case A) [tex](-8,8)\ and\ (2,2)[/tex]
substitute the values in the formula
[tex]m=\frac{2-8}{2+8}[/tex]
[tex]m=\frac{-6}{10}[/tex]
[tex]m=-\frac{3}{5}[/tex]
[tex]-\frac{3}{5}=-\frac{3}{5}[/tex] --------> the ordered pair could be on a parallel line
case B) [tex](-5,-1)\ and\ (0,2)[/tex]
substitute the values in the formula
[tex]m=\frac{2+1}{0+5}[/tex]
[tex]m=\frac{3}{5}[/tex]
[tex]-\frac{3}{5} \neq \frac{3}{5}[/tex]--------> the ordered pair could not be in a parallel line
case C) [tex](-3,6)\ and\ (6,-9)[/tex]
substitute the values in the formula
[tex]m=\frac{-9-6}{6+3}[/tex]
[tex]m=\frac{-15}{9}[/tex]
[tex]m=-\frac{5}{3}[/tex]
[tex]-\frac{3}{5} \neq -\frac{5}{3}[/tex]--------> the ordered pair could not be in a parallel line
case D) [tex](-2,1)\ and\ (3,-2)[/tex]
substitute the values in the formula
[tex]m=\frac{-2-1}{3+2}[/tex]
[tex]m=\frac{-3}{5}[/tex]
[tex]m=-\frac{3}{5}[/tex]
[tex]-\frac{3}{5} =-\frac{3}{5}[/tex]--------> the ordered pair could be on a parallel line
case E) [tex](0,2)\ and\ (5,5)[/tex]
substitute the values in the formula
[tex]m=\frac{5-2}{5-0}[/tex]
[tex]m=\frac{3}{5}[/tex]
[tex]-\frac{3}{5} \neq \frac{3}{5}[/tex]--------> the ordered pair could not be in a parallel line
therefore
the answer is
[tex](-8,8)\ and\ (2,2)[/tex]
[tex](-2,1)\ and\ (3,-2)[/tex]
I believe this would be your answer.
(-8, 8) and (2, 2)
(-2, 1) and (3, -2)
