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Graphing Linear Inequalities
Objectives
1.) To write inequalities to resemble standard linear
equations form y = mx +b
2.) To graph linear inequalities using the steps of graphing
the boundary line and shading the solution area by testing
a point.
Warm-ups
1.) Graph the inequality 2x + 1 > 3 on a number line.
2.) Graph the inequality
on
x
 10
5
a number line.
3.) Write the equation in standard linear equation form
and graph it: x – y = 4
4.) Write the equation in standard linear equation form
and graph it: 2y – x = -10
5.) Write the equation in standard linear equation form
and graph it: y – x = 4
Vocabulary
• Linear inequality: a linear sentence where instead
of having an _______, you have a _____________
• Boundary Line: A dashed or solid line separating
the coordinate plane into
__________________________
• Solution: An (x,y) pair that makes the
inequality a _______________ and is in
_______________________________
Linear Inequality
• A linear inequality
describes an area of
___________________
on the coordinate plane
that has a linear
equation
______________.
• Every point in that
___________region is a
solution of the
inequality.
Consider y > x
Are the following
points solution
points?
(0,0)
(2, -2)
(-1, 2)
(-2, 0)
Getting it in STANDARD LINEAR EQUATION
FORM : Goal is to get y by itself
1.) Solve the equation for y (if necessary).
Example : 3y – 9x ≥ -3




 Get the y and x on separate
sides of inequality. Add 9x to
both sides and simplify
 Addition is commutative
3y 9x  3
 Undo any multiplication or

3
3
division done unto the y to get
y by itself.
 Divide/ Multiply ALL terms and
simplify
Graphing the Linear Boundary
2.) Graph the linear equation just like you would
if it had and an “=“ sign
3.) Draw the line
___________ if the
inequality is ≤ or ≥
4.) Draw the line
____________ if the
inequality is < or >
y  3x  1
5
5
-5
-5
Shade the solution Area
5.) Pick a point not on the line to use as a
________________
The point (0,0) is a good test point if it
________________________
Shade the Solution Set
• If the point makes the
inequality true, shade
that side of the line.
• If the point does not
make the inequality
true, shade the
opposite side of the
line.
Slide Title – Conclusion
•
•
•
•
•
•
We learnt how to graph an inequality
It is similar to graphing an Equation.
Write the inequality in slope intercept form.
Graph the equation.
Check a point on either side of the line.
Shade the solution set.