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