Answer:
Option A and D are correct
(–8, 8) and (2, 2), (–2, 1) and (3, –2)
Step-by-step explanation:
Parallel line:
In parallel lines, the two lines have the same slope and will never intersects.
Using the slope formula:
[tex]\text{Slope} = \frac{y_2-y_1}{x_2-x_1}[/tex] ....[1]
As per the statement:
A line has a slope of -3/5.
We have to find which ordered pairs could be points on a parallel line.
A.
(–8, 8) and (2, 2)
Substitute in [1] we have;
[tex]\text{Slope} = \frac{2-8}{2-(-8)}[/tex]
⇒[tex]\text{Slope} = \frac{-6}{10}= -\frac{3}{5}[/tex]
Similarly for:
B.
(–5, –1) and (0, 2)
Substitute in [1] we have;
[tex]\text{Slope} = \frac{2-(-1)}{0-(-5)}[/tex]
⇒[tex]\text{Slope} = \frac{3}{5}= \frac{3}{5}[/tex]
C.
(–3, 6) and (6, –9)
Substitute in [1] we have;
[tex]\text{Slope} = \frac{-9-6}{6-(-3)}[/tex]
⇒[tex]\text{Slope} = \frac{-15}{9}=- \frac{5}{3}[/tex]
D.
(–2, 1) and (3, –2)
Substitute in [1] we have;
[tex]\text{Slope} = \frac{-2-1}{3-(-2)}[/tex]
⇒[tex]\text{Slope} = \frac{-3}{5}= -\frac{3}{5}[/tex]
E.
(0, 2) and (5, 5)
Substitute in [1] we have;
[tex]\text{Slope} = \frac{5-2}{5-0}[/tex]
⇒[tex]\text{Slope} = \frac{3}{5}=\frac{3}{5}[/tex]
Therefore, the ordered pairs could be points on a parallel line are:
(–8, 8) and (2, 2)
(–2, 1) and (3, –2)
