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

An easy way to compute this is to find the equation of the line and plug each one of the points in for x and y, your answers would be (-2,2) (-1,3) and (-5,-1)

Answer 2

(-1, 3), (-2, 2) and (-5, -1) lie on the line.

Explanation:

Let the equation of the line which is parallel to the given line is y = mx + c

Here m is the slope of line similar to the line given = (y - y')/(x - x')

Here (x, y) and (x', y') are (4, 2) and (-2, -4)

then m = (2+4)/(4+2) = 6/6 = 1

Now the equation of the line will be y = x + c

This line passes through point P(0, 4)

4 = 1×0 + c

c = 4

Therefore equation of the line will be

y = x + 4

Now we check for each point given in the question whether it lies on the line or not.

For (-4, 2)

y = (-4) + 4 = 0

Hence not lies on the line.

For (-1, 3)

y = (-1) + 4 = -1 +4 = 3

Hence (-1,3) lies on the line.

For (-2, 2)

y = (-2) + 4 = -2 + 4 = 2

Hence (-2, 2) lies on the line.

For (4, 2)

y = 4 + 4 = 8

Hence (4, 2) lies on the line.

For (-5, -1)

y = -5 + 4 = -1

Hence (-5, -1) lies on the line.

Therefore (-1, 3),(-2, 2) and (-5, -1) lie on the line.