What is an equation in slope intercept form for the line that passes through the points (1,-3) and (3,1)

Y=2x-5.
I found the slope using the formula m=y2-y1/x2-x1.
m=-3-1/1-3=-4/-2=2.

I used (3,1) (only use one point, your choice) to find out b. 3=x, 1=y.
y=mx+b is the formula for slope intercept equations, so I plugged in the x and y.
1=2(3)+b; 1=6+b, subtract 6 on both sides and get -5=b.
I used the information to get y=2x-5.
Hope this isn’t too confusing! :)