1.5 Representing Linear Patterns

Objectives: Represent linear patterns with equations. Represent linear equations with graphs.

Standards Addressed: 2.8.8.G: Represent relationships with tables or graphs in the coordinate

plane and verbal or symbolic rules. 2.8.8.A: Apply simple algebraic patterns to basic number theory and

to spatial relations.

Ex. 1a.

Ex. 1b.

When the graph is a straight line, the equation is called a linear equation.

In the equation d = 53t, t is the independent variable, and d is the dependent variable.

On a graph, the independent variable is represented on the horizontal axis and the dependent variable is represented on the vertical axis.

Ex. 2a. A jet airplane is flying at a rate of 280 miles per hour. Write a linear equation to express the distance traveled in a given amount of time. Graph the equation for times from 0 to 10 hours.

D = RT D = 280T

X TIME

Y DISTANCE

0 0

2 560

5 1400

10 2800

Ex. 2b. A passenger train averages 54 mph. Write a linear equation that represents the distance traveled in a given time. Graph the equation for times from 0 to 15 hours.

D = R T D = 54 T

X Time Y Distance

1 54

4 216

7 378

9 486

12 648

15 810

Ex. 2c. Jeremy drives at an average rate of 50 mph. Write a linear equation to express the distance he travels in a given amount of time. Graph the equation for times from 0 hours to 10 hours.

D = RT D = 50 T

X Y

0 0

2 100

4 200

6 300

8 400

10 500

Ex. 3