Question

Which points lie on the line that passes through point P and is parallel to the given line? Check all that apply.

(–4, 2)
(–1, 3)
(–2, 2)
(4, 2)
(–5, –1)

Answer 1

(-1,3), (-2,2), and (-5,-1)

Answer 2

Points lie on line: (-1,3), (–5, –1), (–2, 2)

B, C and E are correct

Explanation:

Given: A graph of line and a point P(0,4)

Equation of given line, Points on line are (4,2) and (-2,-4)

`y-2=(2+4)/(4+2)(x-4)`

`y=x-2`

Now, we find the equation of line parallel to given line and passing through point P(0,4)

Slope of parallel line is equal.

Slope = 1 , Point: (0,4)

Equation of line:

`y-4=1(x-0)`

`y=x+4`

Now, we choose the option which passes through the line.

Option 1: (-4,2) Put x=-4 and y=2 into y=x+4

2 = -4 + 4

2 ≠ 0

False

Option 2: (-1,3) Put x=-1 and y=3 into y=x+4

3 = -1 + 4

3 = 3

True

Option 3: (-2,2) Put x=-2 and y=2 into y=x+4

2 = -2 + 4

2 = 2

True

Option 4: (4,2) Put x=4 and y=2 into y=x+4

2 = 4 + 4

2 ≠ 8

False

Option 5: (-5,-1) Put x=-5 and y=-1 into y=x+4

-1 = -5 + 4

-1 = -1

True