Algebra writing an equation with two given points

Could someone help me with this?

Write an equation of a line passing through the points (1,-2) an (-3,1)

The change in X is from 1 to -3; that is a change of -4.
The change in Y is from -2 to 1; that is a change of +3.

So the equation is Y = (+3)/(-4)X + C

In order to find the value of "C", we plug in one of the points. Like this:
-2 = (-3/4)(1)+ C
So then
-2 = (-3/4) +C

Add 3/4 to both sides:
-2 +3/4 = C
-(1 & 1/4) = C

The whole equation is this:
Y = (-3/4)X - (1 & 1/4)

First find 'm' (aka the slope) (-2-1)/(1- (-3)) m=(-3/4)
Next plug into a generic formula. I prefer point-slope but most teachers teach y=mx+b
Point-Slope
y-(-2)=(-3/4)(x-(1)) Simply according to your teacher

y=mx+b
-2=(-3/4)(1)+b Solve for b
b=(-5/4)
y=(-3/4)x+(-5/4)

Use the slope formula:

(1 - (-2)) / (-3 - 1) = 3/-4 = -3/4

Now find the y intercept:

(1 - b) / (-3 - 0) = -3/4

1 - b = 9/4

-b = 5/4

b = -5/4

y = -(3/4)x - 5/4

or

4y + 3x = -5