Slope-intercept form is an equation of the form y = mx + b. Using the rules of algebra, you rearrange the terms of the equation so you have y by itself on one side of the equation and everything else on the other side.
First distribute the 2 into the (x-1) term:
y - 3 = 2x - 2
Add 3 to both sides to get the -3 out of the left side of the equation:
y - 3 + 3 = 2x - 2 + 3
Combine the constant terms and you get:
y = 2x + 1
This is now in slope-intercept form. The slope, m, is 2, and the y-intercept, b, is 1.