4-1 Using Graphs to Relate Two Quantities

Quick Review

You can use graphs to represent the relationship between two variables.

Example

A dog owner plays fetch with her dog. Sketch a graph to represent the distance between them and the time.

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Exercises

5. Travel A car's speed increases as it merges onto a highway. The car travels at 65 mi/h on the highway until it slows to exit. The car then stops at three traffic lights before reaching its destination. Draw a sketch of a graph that shows the car's speed over time. Label each section.
6. Surfing A professional surfer paddles out past breaking waves, rides a wave, paddles back out past the breaking waves, rides another wave, and paddles back to the beach. Draw a sketch of a graph that shows the surfer's possible distance from the beach over time.

4-2 Patterns and Linear Functions

Quick Review

A function is a relationship that pairs each input value with exactly one output value. A linear function is a function whose graph is a line or part of a line.

Example

The number y of eggs left in a dozen depends on the number x of 2-egg omelets you make, as shown in the table. Represent this relationship using words, an equation, and a graph.

Look for a pattern in the table. Each time x increases by 1, y decreases by 2. The number y of eggs left is 12 minus the quantity 2 times the number x of omelets made: y = 12 − 2 x . y equals 12 minus 2 x .

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Exercises

For each table, identify the independent and dependent variables. Represent the relationship using words, an equation, and a graph.

7. Paint in Can

   Number of Chairs Painted, p	Paint Left (oz), L
   0	128
   1	98
   2	68
   3	38

8. Game Cost

   Number of Snacks Purchased, s	Total Cost, C
   0	$18
   1	$21
   2	$24
   3	$27

9. Elevation

   Number of Flights of Stairs Climbed, n	0	1	2	3
   Elevation (ft above sea level), E	311	326	341	356

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