The relation between the fuel economy and speed of a given car was recorded. What is the fuel economy at 20mph? Problem of the Day f(20) = 15 c) f(15) = 10 f(45) = 30 d) f(20) = 25

2) D = {-2, 1, 4}; R = {-1, 2, 3, 5}; not a function 24) -13 26) -18 28) -37 Answers to 2-1

Section 2-2 Linear Relations and Functions

Then Now Objectives You analyzed relations and functions. Identify linear relations and functions.

Common Core State Standards Content Standards Common Core State Standards F.IF.4 – For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.9 – Compare properties of two functions each represented in a different way. Mathematical Practices 3) Construct viable arguments and critique the reasoning of others.

Linear Relations: relations that have straight line graphs Linear Relations: relations that have straight line graphs. Nonlinear Relations: relations that are not linear. Linear Equation: an equation that has no operations other than addition, subtraction and multiplication of a variable by a constant. Linear Function: a function with ordered pairs that satisfy a linear equation. Vocabulary

Example 1 State whether each function is a linear function. Explain. g(x) = 2x – 5 f(x) = 5 𝑥+6 p(x) = 𝑥 3 + 2 h(x) = − 3 2 𝑥+ 1 3

The growth rate of a sample of Bermuda grass is given by the function f(x) = 5.9x + 3.25, where f(x) is the total height in inches x days after an initial measurement. If Bermuda grass is 50.45 in. tall, how many days has it been since it was last cut? Is it reasonable to think that this rate of growth can be maintained for long periods of time? Explain. Example 2

The linear function f(C) = 1 The linear function f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit f(C) that are equivalent to a given number of degrees Celsius C. On the Celsius scale, normal body temperature is 37°C. What is it in degrees Fahrenheit? Example 2

The linear function f(C) = 1 The linear function f(C) = 1.8C + 32 can be used to find the number of degrees Fahrenheit f(C) that are equivalent to a given number of degrees Celsius C. There are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees between these two points. How many Fahrenheit degrees equal 1 Celsius degree? Example 2

y-intercept: the y-coordinate of the point at which a graph crosses the y-axis. x-intercept: the x-coordinate of the point at which a graph crosses the x-axis. Vocabulary

Example 4 Find the x- intercept and the y-intercept of the graph of 2x + 5y – 10 = 0. Then graph the equation.

Example 4 Find the x- intercept and the y-intercept of the graph of -2x + y – 4 = 0. Then graph the equation.

For what value of C will the graph of the following equation have an x-intercept of 3? y = -Cx – 9 Example 4

p.72 #16 – 24 even, 25, 35 – 39 odd, 41, 42 Homework