Cherese and arie each walk in a straight line between two points. using the points on a map that the girls created, cherese will start at (–8, –7) and will stop at (3, 4). arie will start at (5, –22) and will stop at (–8, 17). which point will cherese and arie both walk through?

We first construct the linear equations of each paths of Cherese and Arie using the formula y=mx+b, where m is the slope and b is the y-intercept. 

Cherese:
m = (y₂-y₁)/(x₂-x₁) = (4--7)/(3--8) = 1
4 = 3 + b
b = 1
y = x + 1 <-- equation 1

Arie: 
m = (y₂-y₁)/(x₂-x₁) = (-22-17)/(5--8) = -3
17 = -3(-8) + b
b = -7
y = -3x -7 <--- equation 2

Using substitution to solve for 2 unknowns:
(x+1) = -3x -7
4x = -8
x = -2

y = -2+1 = -1

The intersection of Cherese and Arie's paths will be in point (-2,-1).

You can also graph your equations and find which point the two lines intersect.