4-6 Graphing Linear Functions Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up Interpret the graph. A rocket is fired into the air. The rocket’s speed increases until gravity gradually slows the rocket and causes it to fall to the ground. Course Graphing Linear Functions Rocket Speed Time y x

Problem of the Day The mean of a, 31, 42, 65, and b is 51. The greatest number is 67 more than the least number. What are the missing numbers? 25 and 92 Course Graphing Linear Functions

Learn to identify and graph linear equations. Course Graphing Linear Functions

Vocabulary linear equation linear function Insert Lesson Title Here Course Graphing Linear Functions

The graph at right shows how far an inner tube travels down a river if the current flows 2 miles per hour. The graph is linear because all the points fall on a line. It is part of the graph of a linear equation. A linear equation is an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph. Linear equations and linear graphs can be different representations of linear functions. A linear function is a function whose graph is a nonvertical line. y x Miles Hours 0 Course Graphing Linear Functions

Only two points are needed to draw the graph of a linear function. However, graphing a third point serves as a check. You can use a function table to find each ordered pair. Course Graphing Linear Functions

Graph the linear function y = 4x - 1. Additional Example 1: Graphing Linear Functions Input RuleOutput Ordered Pair x4x – 1y(x, y) 0 1 –1 4(0) – 1 4(1) – 1 4(–1) – 1 –1 3 –5 (0, –1) (1, 3) (–1, –5) Course Graphing Linear Functions

Additional Example 1 Continued Graph the linear function y = 4x - 1. Place each ordered pair on the coordinate grid and then connect the points with a line. x y 0 –2 – –2 –4 (0, –1) (1, 3) (–1, –5) Course Graphing Linear Functions

Graph the linear function y = 3x + 1. Input RuleOutput Ordered Pair x3x + 1y(x, y) 0 1 –1 3(0) + 1 3(1) + 1 3(–1) –2 (0, 1) (1, 4) (–1, –2) Check It Out: Example 1 Course Graphing Linear Functions

Check It Out: Example 1 Continued Graph the linear function y = 3x + 1. Place each ordered pair on the coordinate grid and then connect the points with a line. x y 0 –2 – –2 –4 (0, 1) (1, 4) (–1, –2) Course Graphing Linear Functions

The fastest-moving tectonic plates on Earth move apart at a rate of 15 centimeters per year. Scientists began studying two parts of these plates when they were 30 centimeters apart. Write a linear function that describes the movement of the plates over time. Then make a graph to show the movement over 4 years. Additional Example 2: Earth Science Application Begin by making a function table. Include a column for the rule. Course Graphing Linear Functions

Additional Example 2 Continued InputRuleOutput 15(x) + 30 x (0) (2) (4) + 30 y Let x represent the input and y represent the output. Course Graphing Linear Functions Multiply the input by 15 and then add 30. The function is y = 15x + 30, where x is the number of years and y is the total centimeters apart the two plates are.

Additional Example 2 Continued Graph the ordered pairs (0, 30), (2, 60), and (4, 90) from your table. Connect the points with a line. x Course Graphing Linear Functions Centimeters Years

Check It Out: Example 2 Insert Lesson Title Here Dogs are considered to age 7 years for each human year. If a dog is 3 years old today, how old in human years will it be in 4 more years? Write a linear equation which would show this relationship. Then make a graph to show how the dog will age in human years over the next 4 years. Course Graphing Linear Functions Begin by making a function table. Include a column for the rule.

Check It Out: Example 2 Continued Insert Lesson Title Here InputRuleOutput 7(x) + 21 x (0) (2) (4) + 21 y Course Graphing Linear Functions Let x represent the input and y represent the output. Multiply the input by 7 and then add 21. The function is y = 7x + 21, where x is the number of years and y is the total age of the dog in human years.

Check It Out: Example 2 Continued Insert Lesson Title Here x Course Graphing Linear Functions Graph the ordered pairs (0, 21), (2, 35), and (4, 49) from your table. Connect the points with a line. Human Year Years

Lesson Quiz: Part I Graph the linear functions. 1. y = 3x – 4 2. y = –x y = 2 Insert Lesson Title Here y = 3x – 4 y = –x +4 y = 2 Course Graphing Linear Functions

Lesson Quiz: Part II 4. The temperature of a liquid is decreasing at a rate of 12°F per hour. Susan begins measuring the liquid at 200°F. Write a linear function that describes the change in temperature over time. Then make a graph to show the temperature over 5 hours. y = 200 – 12x Insert Lesson Title Here Course Graphing Linear Functions