Chapter 1: Linear relations
and functions
Section 1-8: Graphing Linear
Inequalities
Linear inequality
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It is NOT a function.
First graph the boundary line
Is the boundary line solid or dashed (Solid if
includes the points ≤ and ≥ and dashed if it
does not include the points <,>)
Now test a point not on the line and see if
the equation holds true. If it does, shade
that side. If not, shade the other side.
Example #1
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Graph x ≤ 2 . The boundary line will be x=2. It will be
a solid line. X=2 is a vertical line. Draw the solid vertical
line. Now test a point not on the line. Test (0,0). When
x=0, does the equation hold true?
Is this true
0 ≤ 2 ? Yes. Therefore shade that side.
Example #2
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Graph x-2y<8
Boundary line x-2y=8 will be dashed because it does not
include the points on the line (<). Draw the line.
(0,0) is not on the line so test that point to see if it makes
the equation true.
0-2(0)<8. Yes. So shade the side (0,0) is on.
Example #3
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Graph y ≤ x + 1
The boundary equation is y= x + 1 . This is an absolute value function
and it’s graph is V shaped. It will also be solid rays because it includes
the points on the rays. Since (0,0) is not on the rays, we will test that
point to see if it makes the inequality true. 0 ≤ 0 + 1 . YES. So shade
that area.
HW #7
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Section 1-8
Pp. 55-56
#9,10,11,14,15,29,30