How does y increase as x increases on the graph y=x-1 and y=2x-1

The increase in y compared to that of x in a linear equation is called the slope.

In an equation in the form y = mx + b, the slope is m.

For y = x - 1, the slope is 1. (the 1 is implied, since x = 1x)
As a fraction, this would be 1/1.
Slope is written as rise over run, or change in y over change in x.
Therefore, as x increases by 1, y increases by 1.

For y = 2x - 1, the slope is 2.
As a fraction, this would be 2/1.
Slope is written as rise over run, or change in y over change in x.
Therefore, as x increases by 1, y increases by 2.