Question 161588
The idea is to convert each equation into the "slope-intercept" form of a line:
y = mx + b
where
m is slope
b is y-intercept at (0,b)
.
Once you do that, it is easy to identify the slope.
.
1st equation (is already there just rearrange):
x+13=y
y = x + 13
or, you can write:
y = (1)x + 13
Now, you can see that the slope of equation 1:
m = 1
.
2nd equation:
y-x=-9
move the x to right by adding x to both sides:
y = x-9
again, you can write:
y = (1)x-9
Now, you can see that the slope of equation 2:
m = 1
.
If two lines are parallel, their slopes must be the same.  Since both equations have the same slope of 1, the two equations are parallel.