Warm Up

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Warm Up

• Write each equation in slope-intercept form.
• 3x 2y -12
• -8 4y x

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Warm Up Answers
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Learn to graph inequalities on the coordinate
plane.
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(No Transcript)
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When the equality symbol is replaced in a linear
equation by an inequality symbol, the statement
is a linear inequality. Any ordered pair that
makes the linear inequality true is a solution.
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There are two types of lines dotted/dashed or
solid. Use solid lines for y gt mx b y lt
mx b.
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There are two types of lines dotted/dashed or
solid. Use dotted/dashed lines for y gt mx b
y lt mx b.
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There are two types of shading shade above the
line or shade below the line. Shade above the
line for y gt mxb y gt mxb.
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There are two types of shading shade above the
line or shade below the line. Shade below the
line for y lt mxb y lt mxb.
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The entire point of graphing Inequalities in two
variables is to show where points are solutions
and to show where points are not solutions.
(-2,4) 4 gt 2(-2) 3 4 gt -1 true (0,3) 3 gt
2(-2) 3 3 gt -1 true (1,1) 1 gt 2(1) 3 1 gt 5
false
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Notice where points are solutions and where
points are not solutions.
(0,0) 0 gt -3(0) -4 0 gt -4 true (-3,-1) -1 gt
-3(-3) -4 -1gt 5 false (1,1) 1 gt 2(1) 3 1 gt 5
false
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Notice where points are solutions and where
points are not solutions.
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Notice where points are solutions and where
points are not solutions.
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Check It Out Example 1A
Graph each inequality. y lt x 4
First graph the boundary line y x 4. Since no
points that are on the line are solutions of y lt
x 4, make the line dashed. Then determine on
which side of the line the solutions lie.
(0, 0)
Test a point not on the line.
y lt x 4
Substitute 0 for x and 0 for y.
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Check It Out Example 1A Continued
Since 0 lt 4 is not true, (0, 0) is not a
solution of y lt x 4. Shade the side of the line
that does not include (0, 0).
(0, 0)
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Check It Out Example 1B
y gt 4x 4
First graph the boundary line y 4x 4. Since
points that are on the line are solutions of y ?
4x 4, make the line solid. Then shade the part
of the coordinate plane in which the rest of the
solutions of y ? 4x 4 lie.
(2, 3)
Choose any point not on the line.
Substitute 2 for x and 3 for y.
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Check It Out Example 1B Continued
Since 3 ? 12 is not true, (2, 3) is not a
solution of y ? 4x 4. Shade the side of the
line that does not include (2, 3).
(2, 3)
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Check It Out Example 1C
3y 4x ? 9
First write the equation in slope-intercept form.
3y 4x ? 9
3y ? 4x 9
Subtract 4x from both sides.
Divide both sides by 3.
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Check It Out Example 1C Continued
(0, 0)
Choose any point not on the line.
Substitute 0 for x and 0 for y.
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Lesson Quiz Part I
Graph each inequality. 1. y lt x 4
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Lesson Quiz Part II
2. 4y 2x gt 12
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Lesson Quiz Part III
Tell whether the given ordered pair is a solution
of each inequality. 3. y lt x 15 (2, 8) 4. y ?
3x 1 (7, 1)
yes
no