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Example 1
This region represents the inequality y<2x−5. We started off by
drawing a dashed line of y=2x-5 (the line is dashed because the
inequality contains a < sign and not a ≤ sign). Then We replaced x
and y in the equation with (0,0). Since 0<-5 is not correct, the point
(0,0) cannot be in the region. As a result, you must shade out the
side where this point is and put an R on the other side to show
that this is the region.

Example 2
This region represents the inequality y≥5x−1. The first step was to
draw a line of the equation y=5x-1. This time the line is not dashed
as the inequality contains a greater than or equal to sign. We
again used the origin (0,0) and substituted it with x and y. We got
0≥−1. Since this inequality is correct, we shade the opposite side
of the line and put an R onto the side with the origin to show that
the region of this inequality is on this side of the line.

R

R

R

R

Example 1
This region represents the inequality y<x²−3x+2. First we drew the
parabola of y=x²-3x+2 with a dashed line since we have y < sign.
The we checked if the origin is in the region of the inequality by
substituting x and y by (0,0): 0<2. Since the inequality is correct
and the origin is outside of the parabola, the area inside the
parabola has to be shaded out. You can put an R in the region that
is not shaded to show that this is the region of the inequality.

Example 2
This region represents the inequality y≥-2x²-x+2. The first thing we
have to do is draw the parabola for y=2x²-x+2 using a normal line
as we have the ≥ sign in the inequality. Then we replace x and y
with the co-ordinates of the origin (0,0) to check if the origin is in
the region: 0≥2. Since this inequality is incorrect, the origin cannot
be in the region. The origin is inside the parabola. Consequently,
we have to shade out the interior of the parabola. We can put an R
outside the parabola to show that this is the region of the
inequality.

R

R

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Chapter 18.2: Learning Outcomes
Students will learn how to represent linear inequalities as regions!
Students will learn how to represent quadratic inequalities as regions!

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