Graph each point on the same coordinate plane.

1. A(-1,2)2. B(4,7)3. C(-3,0)4. D(0,3)

5. Refer to Exercises 1-4. Which equation below gives the relationship between pair of x and y-coordinates?

a. y= 3xb. y = -3xc. y= x + 3d. y = x -3

Bellwork

Algebra 2Sec 1

Tables and Graphs of Linear Equations

Objectives:

• Represent a real-world linear relationship in a table, graph, or equation.

• Identify linear equations and linear relationships between variables in a table.

Linear relationships between two variables occur in a wide variety of situations. For example, the wages of a salesperson who earns a commission are often linearly related to the dollar amount of his or her sales.

Why:

Example 1:

An attorney charges a fixed fee of $250 for an initial meeting and $150 per hour for all hours worked after that.

a) Write an equation to model this situation.

b) Make a table of the total charge for 1, 2, 3, and 4 hours worked.

c) Graph the points and connect them.

d.) Find the charge for 25 hours of work.

A plumber charges a base fee of $55 for a service call plus $35 per hour for all hours worked during the call.

a) Write an equation to model this situation.

b) Make a table of the total charge for 1, 2, 3, and 4 hours worked.

c) Graph the points and connect them.

d) Find the charge for 5 hours of work.

Try This:

NOTES

The previous examples had common characteristics.

Total amount = variable amount + fixed amount

The relationship can be written as y = mx + b. It is called a linear equation. The graph of a linear equation is a straight line.

EXAMPLE 2: Determine whether an equation is a linear equation.1. y = x + 4

2. y = 2x² + 1

3. y = 2/x

4. 5x-2y=7

TRY THIS: Determine whether an equation is a linear equation.

1. y = -4x

2. 3.

4. y = x + 5

EXAMPLE 3: Determine whether a table represents a linear equation.

x 5 6 7 8 9

y 12 14 16 18 20

TRY THIS: Determine whether each table represents a linear equation.

x 7 8 9 10 11

y 11 8 5 2 -1

x 2 3 4 5 6

y 3 4 6 9 13

HomeworkLesson 1

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