First we plot the boundary, whose equation is just like the inequality except
the ≤ is replaced by =.
We plot the line whose equation is
y=2x+2
by getting two points on the line.
x|y
0|?
?|0
if x=0, we substitute 0 for x:
y=2(0)+2
y=2
x|y
0|2
?|0
if y=0, we substitute 0 for y
0=2x+2
-2=2x
-1=x
x|y
0|2
-1|0
So we plot the points (0,2) and (-1,0)
We draw a SOLID line through those two points, SOLID, not DOTTED,
because the inequality is ≤ and not < . Since ≤ includes =, the
graph will contain its boundary line as well as the shaded part.
We pick a test point which is NOT on the line to substitute in the
original inequality to see which side of the line the solutions lie
on. The easiest test point to pick is (0,0), the origin and we can
pick it as long as the line does not pass through the origin. The
line does not pass through the origin so we will substitute (0,0)
in the inequality:
y≤2x+2
0≤2(0)+2
0≤2
This is true, so the test point (0,0) is a solution and so all the
solutions will be on the same side of the line that the origin is on.
The origin is on the lower right side of the line so we will shade
that side of the line:
That graph is the answer!
Edwin
