use the slope and y-intercept to graph each line and tell the point of intersection

y=-x+8
y= x-2

The slope, intercept form is

y = m x + b
Both of these equations are already in that form.
I will just do the first one.
m = slope = -1
b = intercept = 8
so start at x = 0, y = 8 (0,8)
that is your first point.
now go right one and down one.
that point (1,7) is your second point.
Take a straight edge and draw it.
The x axis intercept is where y = 0 so your line should turn out to go through that intercept which is at
0 = -x +8
or x = 8
so make sure it also goes through (8,0)