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