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Graph linear equations Objective Graph linear equations Example 6-3c

A relationship where one thing depends on another Vocabulary Function A relationship where one thing depends on another Example 6-3c

Vocabulary Function table An organized method of the input numbers, output numbers, and the function rule Input Function Output Domain Rule Range Example 6-3c

Vocabulary Domain The set of input values Example 6-3c

The set of output values Vocabulary Range The set of output values Example 6-3c

An equation, when graphed, forms a straight line Vocabulary Linear equation An equation, when graphed, forms a straight line Example 6-3c

A pair of numbers used to locate a point in a coordinate system Review Vocabulary Ordered pair A pair of numbers used to locate a point in a coordinate system Example 6-3c

Example 1 Make a Function Table Example 2 Graph Solutions of Linear Equations Example 3 Represent Real-World Functions Lesson 6 Contents

WORK Asha makes $6. 00 an hour working at a grocery store WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours. Make a function table Label columns Input Function Output 1/3 Example 6-1a

$6.00 an hour total earnings hours WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours. $6.00 an hour total earnings hours Identify the input Identify the function Identify the function Input Function Output Total Earnings ($) Number of Hours Multiply by 6 1/3 Example 6-1a

Put number of hours in the input column WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours. hours Put number of hours in the input column Input Function Output Total Earnings ($) Number of Hours Multiply by 6 1 2 3 4 1/3 Example 6-1a

Multiply the input by 6 to find the output WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours. Multiply the input by 6 to find the output Input Function Output Total Earnings ($) Number of Hours Multiply by 6 1 1  6 6 2 2  6 12 3 3  6 18 4 4  6 24 1/3 Example 6-1a

WORK Asha makes $6. 00 an hour working at a grocery store WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours. Answer: Input Function Output Total Earnings ($) Number of Hours Multiply by 6 1 1  6 6 2 2  6 12 3 3  6 18 4 4  6 24 1/3 Example 6-1a

MOVIE RENTAL Dave goes to the video store to rent a movie MOVIE RENTAL Dave goes to the video store to rent a movie. The cost per movie is $3.50. Make a function table that shows the amount Dave would pay for renting 1, 2, 3, and 4 movies. Answer: Input Function Rule Output Number of Movies Multiply by 3.50 Total Cost ($) 1 3.50  1 3.50 2 3.50  2 7.00 3 3.50  3 10.50 4 3.50  4 14.00 1/3 Example 6-1b

Make a table with 4 columns Label 1st column as “x” Graph Label 2nd column with the rule Label 3rd column as “y” x x + 3 y 2/3 Make a table with an x column, a rule column, a y column, and an ordered pair column Example 6-2a

Label 4th column as the ordered pairs (x, y) Graph Select any four values for the input x I choose 2, 1, 0, and -1 because they are small and easy x x + 3 y (x, y) 2 2 + 3 5 (2, 5) Substitute the value of x into the function column 1 1 + 3 4 (1, 4) Make the ordered pairs from the x and y columns 0 + 3 3 (0, 3) -1 -1 + 3 2 (-1, 2) 2/3 Example 6-2a

Graph the ordered pairs Label ordered pairs (2, 5) Graph (1, 4) Graph the ordered pairs (0, 3) Label ordered pairs (–1, 2) x x + 3 y (x, y) 2 2 + 3 5 (2, 5) 1 1 + 3 4 (1, 4) 3 0 + 3 (0, 3) -1 -1 + 3 2 (-1, 2) 2/3 Example 6-2a

Draw a line connecting the dots (2, 5) Graph (1, 4) Draw a line connecting the dots (0, 3) (–1, 2) x x + 3 y (x, y) 2 2 + 3 5 (2, 5) 1 1 + 3 4 (1, 4) 0 + 3 3 (0, 3) -1 -1 + 3 2 (-1, 2) 2/3 Example 6-2a

Graph Answer: x x + 3 y (x, y) 2 2 + 3 5 (2, 5) 1 1 + 3 4 (1, 4) 0 + 3 (0, 3) (–1, 2) x x + 3 y (x, y) 2 2 + 3 5 (2, 5) 1 1 + 3 4 (1, 4) 0 + 3 3 (0, 3) -1 -1 + 3 2 (-1, 2) 2/3 Example 6-2a

Ordered pairs will vary depending on your choice for x but the line should be alike Graph Answer: 2/3 Example 6-2b

Draw a function table with 4 columns t 30t d ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph. Draw a function table with 4 columns t 30t d Label the 1st column with t for time Label the 2nd column with the rule Label the 3rd column with the output for distance d 3/3 Example 6-3a

Label 4th column with the ordered pairs t 30t d (t, d) ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph. Label 4th column with the ordered pairs t 30t d (t, d) 1 Choose 4 values for the time 2 I choose 1, 2, 3, and 4 hours because they are easy to graph 3 4 3/3 Example 6-3a

Substitute the input of t into the function t 30t d (t, d) ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph. Substitute the input of t into the function t 30t d (t, d) 1 30  1 30 (1, 30) Find the output d Make ordered pairs from the t and d columns 2 30  2 60 (2, 60) 3 30  3 90 (3, 90) 4 30  4 120 (4, 120) 3/3 Example 6-3a

Graph the ordered pairs Label the horizontal axis Label the vertical axis 140 120 Scale must include 0 - 120 100 80 t 30t d (t, d) 1 30(1) 30 (1, 30) 2 30(2) 60 (2, 60) 3 30(3) 90 (3, 90) 4 30(4) 120 (4, 120) 60 40 20 1 2 3 4 3/3 Example 6-3a

Draw a line through the points 140 Plot each ordered pair Draw a line through the points 140 (4, 120) 120 Answer: 100 (3, 90) 80 t 30t d (t, d) 1 30(1) 30 (1, 30) 2 30(2) 60 (2, 60) 3 30(3) 90 (3, 90) 4 30(4) 120 (4, 120) 60 (2, 60) 40 (1, 30) 20 1 2 3 4 3/3 Example 6-3a

* TRAVEL Susie takes a car trip traveling at an average speed of 55 miles per hour. The equation describes the distance d that Susie travels in time t. Represent this function with a graph. Answer: 3/3 Example 6-3c

Functions and Linear Equations Assignment Lesson 4:6 Functions and Linear Equations 8 - 25 All End of Lesson 6