If it's parallel to x - y = 7, that means the slope of that equation is the slope for the equation you're looking for.
To get the slope, you need to put the given equation into slope intercept form, so move x to the other side. You should get: -y = 7 - x
Then, to get the y positive, divide by -1: y = -7 + x
Slope intercept form is as follows: y = mx + b, so whatever the number is in front of x is your slope. In this instance, your slope is 1.
You now have your slope, and a point in which your new line passed through. Using slope intercept form, y = mx + b, if you substitute in what you know, you can find your answer. Right now you know y, m, and x, and you're looking for b.
x=1; y=0; m=1.
So, substituting, you'd get 0 = (1)(1) + b
0=1+b Solve
You should get b= -1, leaving your final answer as y = x - 1
