Word problem systems of equations 8th grade math

Question

A car and a limo each drive along a straight road between two points. Using the points on a map that the city created, the car will start at (5,7) and will stop at (-2, -7), while the limo will start at (3,-5) and will stop at (-4,9). What are the coordinates of the intersection that the car and the limo both drive through?

Answer 1

(5,7), (-2,-7) have a line through them with slope = 14/7 = 2

y= 2x + b

7 = 10+b

b =-3

y =2x -3

(3,-5), (-4,9) has slope=-2= (y-9)/(x+4)

y= -2x+1

intersection is where -2x+1=2x-3

x=1, y= -1

(1,-1)