1.1 Tables and Graphs of Linear Equations Objective: To identify linear equations/relationships and...

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

A

B

C

D

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.

a) 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.

a) 1 64 2 73 3 82 4 91

c) W = 9m + 55

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

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

• Not linear

33 xy33 1 xy

24 2 xy

65 xy

Example 2

• Graph 132 xy

Example 2

• Graph

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

132 xy

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

You Try

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

345 xy

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

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 7.4

1 2

No. Not a constant difference for y.

4

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.

xy 31533$

Yes. )48,11(

Class work

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

Homework

• Pages 8-9• 7-39 odd, 51