Question

Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables.

Answer 1

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Slope of the first is chg y/chg x or 4/2=2
now use point slope formula y-y1=m(x-x1), where m is the slope and (x1,y1) is the point.
y-3=2(x-0)
y=2x+3

The other
slope is 2/-2=-1
y-5=-1(x-1)
y-5=-x+1
y=-x+6

Slopes aren't the same or a negative reciprocal, so they intersect. Coincident.
substitute the second into the first
-x+6=2x+3
3x=3
x=1
Therefore, y=2(1)+3=5. The point is (1,5) where they intersect.
Check with the second
5=-1+6, check