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