What is the equation of the line that passes through (4,-1) and (-2,3)

A straight line has the equation: y = mx + c

The two coordinates can be used to find the slope, m.
 \frac{y2-y1}{x2-x1} 
Where (4, -1) and (-2, 3) make x1 = 4 and x2 = -2, and y1 = -1 and y2 = 3

Sub those values in:
 \frac{3--1}{-2-4} 
 \frac{4}{-6}
So m = 4/-6 = 2/-3 = -2/3

Putting that into y = mx + c, to make: y = (-2/3)x + c
We now need to find c, we can do this by subbing either coords into it.
I choose (4, -1): so x = 4 and y = -1

y = (-2/3)x + c
-1 = (-2/3)(4) + c
-1 = -8/3 + c
-3/3 = -8/3 + c
5/3 = c

So the equation is: y = (-2/3)x + 5/3