Which points lie on the line that passes through point P and is parallel to the given line? Select three options. (–4, 2) (–1, 3) (–2, 2) (4, 2) (–5, –1)

So we have (-1,3), (-2,2) and (-5,-1).

Step-by-step explanation:

So we need to find the equation of the line that is parallel to the blue line going through point P.

The slope of the blue line (count the rise/run) is 1/1=1.

Parallel lines have the same slope.  

So y=mx+b is the slope-intercept form where m is the slope and b is the y-intercept.

So since the blue line has slope 1 and parallel lines have the same slope then the line going through point P will have slope 1 too.

Point P is actually the y-intercept of the line going through P.

So the equation that is parallel to the blue line going through point P is y=1x+4. b was 4 because it was the y-intercept.

You can also just write y=1x+4 as y=x+4.

Testing the points:

(-4,2)?

Does y=x+4 for this point?  2=-4+4 which gives us 2=0 so no for this point.

(-1,3)?

Does y=x+4 for this point?  3=-1+4 which gives us 3=3 so yes for this point.

(-2,2)?

Does y=x+4 for this point?  2=-2+4 which gives us 2=2 so yes for this point.

(4,2)?

Does y=x+4 for this point?  2=4+4 which gives us 2=8 so no for this point.

(-5,-1)?

Does y=x+4 for this point?  -1=-5+4 which gives -1=-1 so yes for this point.

So we have (-1,3), (-2,2) and (-5,-1).

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step-by-step explanation: