Graphing Linear Inequalities

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Graphing Linear Inequalities

• slope y-intercept
• x- y- intercepts
• Jeffrey Bivin
• Lake Zurich High School
• Jeff.bivin_at_lz95.org

Last Updated October 11, 2005
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Graphing Linear Inequalities

• Select the desired MENU option below
• Slope and y-intercept
• x- y- intercepts

Jeff Bivin -- LZHS
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Graphing LinearInequalities
slope and y-intercept
Jeff Bivin -- LZHS
4
y 2x 1
y 2x 1
Run
1
y-intercept
Rise
b 1
2
slope
m 2
Jeff Bivin -- LZHS
5
y 2x 1
Now for the shading
y 2x 1
Pick a point on either side of the graph
Lets try (2, 1)
Does the point satisfy the inequality?
Shade
1 2(2) 1
1 4 1
TRUE
1 5
Therefore, shade the half-plane with the point.
Jeff Bivin -- LZHS
6
y 2x 1
What if we picked a point on the other side of
the line?
y 2x 1
Don't Shade
Lets try (-2, 3)
Does the point satisfy the inequality?
Shade
3 2(-2) 1
3 -4 1
3 -3
FALSE
Therefore, shade the otherhalf-plane opposite
the point.
Jeff Bivin -- LZHS
7
y -3x 2
y -3x 2
Run
1
y-intercept
Rise
b 2
-3
slope
m -3
Jeff Bivin -- LZHS
8
y -3x 2
y -3x 2
Now for the shading
Pick a point on either side of the graph
Lets try (0, 0)
Shade
Does the point satisfy the inequality?
Don't Shade
0 -3(0) 2
0 0 2
FALSE
0 2
Therefore, shade the other half-plane opposite
the point.
Jeff Bivin -- LZHS
9
Run
3
y-intercept
b -1
Rise
2
slope
Jeff Bivin -- LZHS
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Now for the shading
Pick a point on either side of the graph
Lets try (0, 0)
Shade
Does the point satisfy the inequality?
TRUE
Therefore, shade the half-plane with the point.
Jeff Bivin -- LZHS
11
Graphing LinearInequalities
x- and y- intercepts
Jeff Bivin -- LZHS
12
2x 3y 5
find the x value when y 0
x-intercept
2x 3(0) 5
2x 0 5
2x 5
find the y value when x 0
y-intercept
2(0) 3y 5
0 3y 5
3y 5
Jeff Bivin -- LZHS
13
2x 3y 5
Now for the shading
Pick a point on either side of the graph
Lets try (4, 2)
Shade
Does the point satisfy the inequality?
TRUE
Therefore, shade the half-plane with the point.
Jeff Bivin -- LZHS
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2x 3y 5
What if we picked a point on the other side of
the line?
Lets try (-3, -4)
Shade
Does the point satisfy the inequality?
Don't Shade
FALSE
Therefore, shade the other half-plane opposite
the point.
Jeff Bivin -- LZHS
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4x - y gt 6
find the x value when y 0
x-intercept
4x - (0) 6
4x - 0 5
4x 6
find the y value when x 0
y-intercept
4(0) - y 6
0 - y 6
-y 6
Jeff Bivin -- LZHS
16
4x - y gt 6
Now for the shading
Pick a point on either side of the graph
Lets try (0, 0)
Does the point satisfy the inequality?
Don't Shade
Shade
FALSE
Therefore, shade the other half-plane opposite
the point.
Jeff Bivin -- LZHS
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4x 2y lt 3
find the x value when y 0
x-intercept
4x 2(0) 3
4x 0 3
4x 3
find the y value when x 0
y-intercept
4(0) 2y 3
0 2y 3
2y 3
Jeff Bivin -- LZHS
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4x 2y lt 3
Now for the shading
Pick a point on either side of the graph
Lets try (0, 0)
Does the point satisfy the inequality?
Shade
TRUE
Therefore, shade the half-plane with the point.
Jeff Bivin -- LZHS
19
3x - 2y lt 7
find the x value when y 0
x-intercept
3x - 2(0) 7
3x - 0 7
3x 7
find the y value when x 0
y-intercept
3(0) - 2y 7
0 - 2y 7
-2y 7
Jeff Bivin -- LZHS
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3x - 2y lt 7
Now for the shading
Pick a point on either side of the graph
Lets try (0, 0)
Does the point satisfy the inequality?
Shade
TRUE
Therefore, shade the half-plane with the point.
Jeff Bivin -- LZHS