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