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.
sidewalk 1
x y
2 7
0 3
sidewalk 2
x y
1 5
3 3
(a) write the equation for sidewalk 1 in slope-intercept form.
(b) write the equation for sidewalk 2 in point-slope form and then in slope-intercept form.
(c) is the system of equations consistent independent, coincident, or inconsistent? explain.
(d) if the two sidewalks intersect, what are the coordinates of the point of intersection? use the substitution method and show your work.

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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

B

Step-by-step explanation: