Algebra I: Section 6.5
Name:________________________
Objective: To graph a linear inequality on the Cartesian plane.
To graph 2x – 4y < 8, you need to give all the solutions.
Is (4,1) a solution of 2x – 4y < 8 ?
How do you check?
There are infinitely many solutions, so it’s best to graph them.
The line 2x – 4y = 8 divides the Cartesian plane into three
regions:
1) the line itself which is the set of all points where
2x – 4y equals 8.
2) one side of the line which is the set of all points
where 2x – 4y is less than 8.
3) the other side of the line which is the set of all
points where 2x – 4y is greater than 8.
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Graphing Inequalities:
1) First, graph the equation. This will serve as the
boundary line.
~Draw it as a regular line for ≥ or ≤ because you
want to include the equation.
~Draw a dotted line for > or <, because you don’t
want the equation but you need to show the
boundary line.
2) Now you must determine which side of the line
to shade in. There are two ways to do this:
~Choose a point not on the line and substitute it into
the inequality. If it produces a true statement, shade
that side. If it does not work, shade in the other side.
You can’t lose.
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f ( x ) = 2!x - 3
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~If you rewrite the inequality as y ≤, <, >, or ≥
mx+b,
a) For < or ≤, you shade in below the line
because y ____________________
b) For > or ≥, you can shade in above the
line because y ____________________
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Graph the following inequalities:
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y > 4 – 3x
2x – 3y ≥ 6
3x – y < 4
What about vertical lines?
x > or ≥ # : When does x get bigger ? _______________
So shade in the region to the ________ of the line.
x< or ≤ #: When does x get smaller?
So shade in the region to the ___________ of the line.
Graph: x ≤ 4
3-2x < 11
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What is being graphed below?
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6.5
pgs.363-366 # 15, 27, 35, 43- 50 all, 63, 64, 65,82