Tables, Graphs, Equations

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1. MA.8.A.1.5Translate among verbal, tabular, graphical and algebraic representations of linear functions. A relation is a set of ordered pairs. If the ordered pairsĀ ...
MA.8.A.1.5 Translate among verbal, tabular, graphical and algebraic representations of linear functions. A relation is a set of ordered pairs. If the ordered pairs form a straight line on a graph, the relation is said to be linear. You can use the graph of a relation to write an algebraic expression that describes it. Example: A plumber charges a flat fee to visit a home and then charges an hourly fee for the amount of time worked. The total amounts of plumbing bills for different numbers of hours worked are shown in the graph.

a. Write an algebraic expression to represent the data in the graph. Write the ordered pairs in a table. Look for a pattern.

The common difference is 35, so 35h is part of the expression. To get the total amount, add 50. The expression is 35h + 50. a. Use the expression to find the total amount of a plumbing bill for 8 hours of work. 35h + 50 = 35(8) + 50 Replace h with 8. = 280 +

Multiply 35 and 8.

50 Simplify. = 330 b. The plumbing bill for 8 hours of work is $330. 1

Translate Tables and Graphs into Equations Example MONEY Malik earns $8.50 per hour washing cars. Write an equation to find how 1 much money m Malik earns for any number of hours h. Let m represent the money earned and h represent the number of hours worked. The equation is m = 8.5h. How much will Malik earn if he works 4 hours? m = 8.5h

Write the equation.

m = 8.5(4)

Replace h with 4.

m = 34

Multiply.

Make a table to find his earnings if he works 7, 8, 9, or 10 hours. Then graph the ordered pairs.

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MA.8.A.1.5 Practice Problems

A. Lourdes earns $6.67 per hour plus tips. B. Lourdes earns $6.67 per hour. C. Lourdes earns $5 per hour. D. Lourdes earns more money per hour the longer she works.

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12. Use the table to write an equation to find the number of inches i in any number of meters m. Use the equation to find the number of inches in 9 meters.

Meters, m

Inches, i

1

39

2

78

3

117

4

156

_____________________________________ 13. Private swimming lessons cost $30 per visit plus $3 per child in the group. Write an equation to find the total cost t of a swimming lesson for any number of children c. Use the equation to find the cost of a lesson for 3 children.

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17. CARS A car dealer sells 12 cars per week. Write an equation to find the number of new cars c sold in any number of weeks w. Make a table to find the number of new cars sold in 4, 5, 6, or 7 weeks. Then graph the ordered pairs. Weeks, w

Cars, c

18. WRITING An author writes four pages per day. Write an equation to find the number of pages p written after any number of days d. Make a table to find the number of pages the author writes in 1, 2, 3, or 4 days. Then graph the ordered pairs. Days, d

Pages, p

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