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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)

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 class=

Respuesta :

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:

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

Step-by-step 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.

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