1.1 Tables and Graphs of Linear Equations Objective: To identify linear equations/relationships and to express them in a table/graph

Warm up

Warm up

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

You Try Look at the problem on the middle of page 5. Try this with a partner or group.

You Try Look at the problem on the middle of page 5. Try this with a partner or group. 1 64 2 73 3 82 4 91

You Try Look at the problem on the middle of page 5. Try this with a partner or group. 1 64 2 73 3 82 4 91 W = 9m + 55

You Try Look at the problem on the middle of page 5. Try this with a partner or group. 1 64 2 73 3 82 4 91 W = 9m + 55 d) 235 = 9(20) + 55

Linear Equation The examples we just looked at have a characteristic in common. Each has the form: total amount = variable amount + fixed amount

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.

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.

Linearly Related This leads to the following definition:

Linear What makes an equation linear? It is the power (degree) or exponent of the x variable.

Linear What makes an equation linear? It is the power (degree) or exponent of the x variable. Linear or Not linear

Example 2 Graph

Example 2 Graph We will look at several ways to graph. For this example, we will pick numbers and plot points.

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

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

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

Using a Table

Example 3

Example 3

Try This Do the two problems in the middle of page 7.

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

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.

Yes.

Class work In groups/pairs, do problems 1-6 on pages 7-8.

Homework Pages 8-9 7-39 odd, 51