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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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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 + 55 d) 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

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Example 2 Graph

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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.

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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

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You Try Try the example in the middle of page 6. Compare your answers to someone sitting near you.

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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

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Using a Table

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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. No. Not a constant difference for y.

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Try This Do the two problems in the middle of page 7. No. Not a constant difference for y. Yes. 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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Yes.

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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

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