Question

A line has a slope of-3/5 . Which ordered pairs could be points on a parallel line? Select two options. (–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)

Answer 1

Solution:

Given => Slope of line = -3/5

To check => To check which ordered pairs could be points on a parallel line from these

(–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)

If two lines are parallel then there slope will also be equal.

Slope tells us about the direction of line.

To find slope of a line,  $m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

Let's apply slope formula on every ordered pair and if the slope comes equal to the original line which is having slope -3/5 then the ordered pair could be points on a parallel line

(–8, 8) and (2, 2)

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

$m = \frac{2 - 8 }{2 - (-8)}}$

$m = \frac{2 - 8 }{2 + 8}}$

$m = \frac{-6 }{10}}$

$m = \frac{-3}{5}}$

This ordered pair slope is equal to original line slope so, this ordered pair could be points on a parallel line.

(–5, –1) and (0, 2)

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

$m = \frac{2 - (-1) }{0 - (-5)}}$

$m = \frac{2 +1 }{0 + 5}}$

$m = \frac{3 }{ 5}}$

This ordered pair slope is not equal to original line slope so, this ordered pair could not be points on a parallel line.

(–3, 6) and (6, –9)

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

$m = \frac{-9 - 6 }{6 - (-3)}$

$m = \frac{-9 - 6 }{6 + 3}$

$m = \frac{-15 }{9}$

$m = \frac{-5 }{3}$

This ordered pair slope is not equal to original line slope so, this ordered pair could not be points on a parallel line.

(–2, 1) and (3, –2)

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

$m = \frac{-2 - 1 }{3 - (-2)}$

$m = \frac{-2 - 1 }{3 + 2}$

$m = \frac{-3 }{5}$

This ordered pair slope is equal to original line slope so, this ordered pair could be points on a parallel line.

(0, 2) and (5, 5)

$m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$

$m = \frac{5 - 2 }{5 - 0}$

$m = \frac{3 }{5 }$

This ordered pair slope is not equal to original line slope so, this ordered pair could not be points on a parallel line.

These two ordered pairs (–8, 8) and (2, 2) , (–2, 1) and (3, –2) will be points on a parallel line.