Linear Relationships

Algebraic Relationships: Equations

Linear Relationships

Linear Relationship

is an algebraic relationship whose graph is a line.

We can show Linear Relationships in:

Graphs

Tables

Equations

IMPORTANT!

• (Independent, Dependent)

• (x , y)

Writing an Equation

You can use an equation to represent an algebraic relationship.

The input or independent variable represents the x-values.

The output or dependent variable represents the y-values.

An equation represents the relationship between the independent and the dependent quantities.

Write an equation from table

• Look at the Input and Outputs.

• Determine how you are going from Input to Output.

• The value y is equal to 9 times the value of x.

• So, the equation that represents the relationship is y = 9(x)

Multiple Choice

Write an equation to represent the relationship between the independent and dependent quantities shown in the table.

• y = x + 16

• y = 16x

• y = 16 - x

• y = x / 16

Representing using Graphs

Problem: Represent y = 2(x) with a graph.

Step 1: make a table to create ordered pairs

Step 2: Graph each ordered pair. Draw a line through it.

Multiple Choice

Represent the relationship, with a graph:

y = x + 3

Multiple Choice

Represent the relationship, with a graph:

y = 3x

Writing Equations from Graphs

Step 1: Select 3 points on the graph

Step 2: Place them in a table

Step 3: Determine a rule for the graph

Ex:

Points: (1,5) (2,10) (3,15)

Rule: each term is x5

Equation: y = 5x

Multiple Choice

Using the graph, write an equation:

• y = 5x

• y = 12 + x

• 6x

• x + 6