The general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables (and the coordinate points on the graph).
Remember that for parallel lines, the slope, m, is the same for both equations. The equation you're given, y = 2x - 2, is already in slope-intercept form and the 2 in front of x is m, your slope. That means for whatever equation we come up with, m has to be 2.
So far we know the equation for our parallel line is y = 2x + b. How do we figure out b? Plug in the (x, y) coordinate you're given, (1, 1) and solve for b:
[tex]y = 2x + b\\
1 = 2(1) + b\\
1 = 2 + b\\
b = -1[/tex]
Now we know b = -1. Put that into our y = 2x + b equation to get the final equation of your parallel line:
Your final answer is y = 2x - 1.
