Question

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)

Answer 1

I believe this would be your answer.

(-8, 8) and (2, 2)

(-2, 1) and (3, -2)

Answer 2

we know that

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

If two lines are parallel, then their slopes are equal

in this problem we have

the slope of the given line is
`m=-(3)/(5)`

if ordered pairs could be points on a parallel line, then the ordered pairs must have a slope equal to
`m=-(3)/(5)`

we are going to calculate the slope in each of the cases

case A)
`(-8,8)\ and\ (2,2)`

substitute the values in the formula

`m=(2-8)/(2+8)`

`m=(-6)/(10)`

`m=-(3)/(5)`

`-(3)/(5)=-(3)/(5)` --------> the ordered pair could be on a parallel line

case B)
`(-5,-1)\ and\ (0,2)`

substitute the values in the formula

`m=(2+1)/(0+5)`

`m=(3)/(5)`

`-(3)/(5) \\eq (3)/(5)`--------> the ordered pair could not be in a parallel line

case C)
`(-3,6)\ and\ (6,-9)`

substitute the values in the formula

`m=(-9-6)/(6+3)`

`m=(-15)/(9)`

`m=-(5)/(3)`

`-(3)/(5) \\eq -(5)/(3)`--------> the ordered pair could not be in a parallel line

case D)
`(-2,1)\ and\ (3,-2)`

substitute the values in the formula

`m=(-2-1)/(3+2)`

`m=(-3)/(5)`

`m=-(3)/(5)`

`-(3)/(5) =-(3)/(5)`--------> the ordered pair could be on a parallel line

case E)
`(0,2)\ and\ (5,5)`

substitute the values in the formula

`m=(5-2)/(5-0)`

`m=(3)/(5)`

`-(3)/(5) \\eq (3)/(5)`--------> the ordered pair could not be in a parallel line

therefore

the answer is

`(-8,8)\ and\ (2,2)`

`(-2,1)\ and\ (3,-2)`