1.1 tables and graphs of linear equations objective: to identify linear equations/relationships and...
TRANSCRIPT
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1.1 Tables and Graphs of Linear Equations
Objective: To identify linear equations/relationships and to express them in a table/graph
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Warm up
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Warm up
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Example 1
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Example 1
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Example 1
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Example 1
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Example 1
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Example 1
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You Try
• Look at the problem on the middle of page 5. Try this with a partner or group.
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You Try
• Look at the problem on the middle of page 5. Try this with a partner or group.
a) 1 64 2 73 3 82 4 91
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You Try
• Look at the problem on the middle of page 5. Try this with a partner or group.
a) 1 64 2 73 3 82 4 91
c) W = 9m + 55
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You Try
• Look at the problem on the middle of page 5. Try this with a partner or group.
a) 1 64 2 73 3 82 4 91
c) W = 9m + 55d) 235 = 9(20) + 55
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Linear Equation
• The examples we just looked at have a characteristic in common. Each has the form:
total amount = variable amount + fixed amount
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Linearly Related
• The examples we just looked at have a characteristic in common. Each has the form:
total amount = variable amount + fixed amount• In general, if a relationship between x and y can be
written as y = mx + b, where m and b are real numbers, then x and y are linearly related.
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Linearly Related
• The examples we just looked at have a characteristic in common. Each has the form:
total amount = variable amount + fixed amount• In general, if a relationship between x and y can be
written as y = mx + b, where m and b are real numbers, then x and y are linearly related.
• The equation y = mx + b is called a linear equation. The graph of a linear equation is a straight line.
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Linearly Related
• This leads to the following definition:
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Linear
• What makes an equation linear? It is the power (degree) or exponent of the x variable.
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Linear
• What makes an equation linear? It is the power (degree) or exponent of the x variable.
• Linear or
• Not linear
• Not linear
33 xy33 1 xy
24 2 xy
65 xy
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Example 2
• Graph 132 xy
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Example 2
• Graph
• We will look at several ways to graph. For this example, we will pick numbers and plot points.
132 xy
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Example 2
• Graph
• We will look at several ways to graph. For this example, we will pick numbers and plot points.
x y 0 -1 3 1
132 xy
1)0(1 32
1)3(1 32
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You Try
• Try the example in the middle of page 6. Compare your answers to someone sitting near you.
345 xy
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You Try
• Try the example in the middle of page 6. Compare your answers to someone sitting near you.
x y 0 3 4 8
345 xy
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Using a Table
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Example 3
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Example 3
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Try This
• Do the two problems in the middle of page 7.
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Try This
• Do the two problems in the middle of page 7.4
1 2
No. Not a constant difference for y.
4
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Try This
• Do the two problems in the middle of page 7.4
1 2
No. Not a constant difference for y.
4
3
0Yes. There is a constant difference for each x and y term. The next x is -9 and the next y is 5.
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xy 31533$
Yes. )48,11(
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Class work
• In groups/pairs, do problems 1-6 on pages 7-8.
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Homework
• Pages 8-9• 7-39 odd, 51