ALGEBRA 5.1 Identifying Linear Functions

Learning Targets Language Goal  Students will be able to identify linear functions and linear equations. Math Goal  Students will be able to graph linear functions that represent real-world situations and give their domain and range. Essential Questions  What is a real-world situation that represents a linear function?

Warm-up

Vocabulary  Linear Function:  Linear Equation: A function whose graph forms a straight line. Any equation that can be written in standard form.

Identifying Linear Functions  There are 3 ways to identify.  By its Graph  By using Ordered Pairs  By its Equation

Identifying by its Graph  Your first step is to identify if the graph is a function  Remember a function is when one domain value is paired with exactly one range value.  You can do the vertical line test!  If the graph is a function, tell whether it is linear.  A linear graph means that it forms a straight line.

Identifying by its Graph  Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear? Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______

Example 1: Your Turn! Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______ Function? __________ If yes, Linear? _______

Identifying by using Ordered Pairs  It might help to write all ordered pairs into a table.  For example: {(2, 5), (4, 8), (6, 11)}  In a linear function, a constant change in x corresponds to a constant change in y. ***Remember both x and y need to have a constant change in values. It does not have to be the same constant! XY

Identifying by using Ordered Pairs XY ExampleNon Example XY Constant change in x and y Linear Function Constant change in x and but not y Not a linear function

Identifying by using Ordered Pairs  Tell whether each set of ordered pairs satisfies a linear function. Explain. A. {(2, 4). (5, 3), (8, 2), (11, 1)}B.{(-10, 10), (-5, 4), (0 2), (5, 0)}

Example 2: Your Turn!  Tell whether each set of ordered pairs satisfies a linear function. Explain. C. {(3, 5). (5, 4), (7, 3), (9, 2), (11, 1)} D.{(0, -3), (4, 0), (8, 3), (12, 6), (16, 9)} E. {(-4, 13), (-2, 1), (0, -3), (2, 1), (4, 13)}

Identifying by using the Equation  If an equation can be written in standard form, then it is a linear equation.  What is standard form? Ax + By = C where A, B, and C are real numbers and A and B are not both 0.

Identifying by using the Equation  Notice that when a linear equation is written in standard form…  x and y both have exponents of 1  x and y are not multiplied together  x and y do not appear in denominators, exponents or radical signs.

Identifying by using the Equation LinearNot Linear Standard Form: Ax + By = C

Practice Re-Writing in Standard Form

Identifying by using an Equation

Example 3: Your turn

Review

Word Application  Sue rents a manicure station in a salon and pays the salon owner $5.50 for each manicure she gives. The amount she pays each day is given by f(x) = 5.50x, where x is the number of manicures. Graph the function and give its domain and range.

Word Application  The relationship between human years and dog years is given by the function y = 7x, where x is the number of human years. Graph this function and give its domain and range.