4-6 Graphing Linear Functions pg. 248

Essential Question How do you determine if a function is a linear function?

Graphing Review Video Clip- Standard Deviants In your notebook: Write down 3 facts from the video clip

Definitions linear equation- an equation whose graph is a line. The solutions of a linear equation are the points that make up its graph. linear function-a function whose graph is a non-vertical line.

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. 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.

A Function (F) states the relationship between two variables. (, ) 2 8 It assigns a rule, that gives a unique value to y in relation to the value of x. Rule Y = 4x

Function RO filter Input Rule Output x 4x y Function y = 4x 4(2) 4(3) 4(4) 4(5)

Rule: y = x Inputoutput I’ll push the pedal once. I’ll push the pedal. Every time you push the pedal, I’ll square your effort in rotations 2

Function RO filter Input Rule Output x x y Function 2 25 y = x

Rule: y = 3x Inputoutput I’ll give 3 gumballs for every quarter I’ll push the pedal once. I’ll put quarters in.

Function RO filter Input Rule Output x 3x y 2 3(2) 3 3(3) 4 3(4) 5 3(5) Function y = 3x

x y 0 –2 – –2 –4 Graph the linear function y = 4x - 1. Example 1 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) (0, –1) (1, 3) (–1, –5)

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) Example 2 x y 0 –2 – –2 –4 (0, 1) (1, 4) (–1, –2)

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. Example 3 InputRuleOutput 15(x) + 30 x (0) (2) (4) + 30 y x Centimeters Years

Graphing Linear Equations Brain-Pop Write down 2 facts about graphing linear equations.  1.  2.

Work Session Linear Contemplations Worksheet Follow along as we review the directions

Homework Workbook pg. 41 All problems

Closing 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