A line has a slope of -3/5 Which ordered pairs could be points on a parallel line? Check all that apply.(–8, 8) and (2, 2)(–5, –1) and (0, 2)(–3, 6) and (6, –9) (–2, 1) and (3, –2) (0, 2) and (5, 5)
Accepted Solution
A:
we know thatThe 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 equalin this problem we havethe 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 casescase 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 linecase 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 linecase 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 linecase 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 linecase 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 linethereforethe answer is[tex](-8,8)\ and\ (2,2)[/tex][tex](-2,1)\ and\ (3,-2)[/tex]