1.5 Representing Linear Patterns

1. 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.

2. Ex. 1a.

3. Ex. 1b.

4. 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.

5. 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

6. 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

7. 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

8. Ex. 3