September 17, 2010. Objectives Students will be able to: Identify linear equations and functions, Write linear equations in standard form and graph them.

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Presentation transcript:

September 17, 2010

Objectives Students will be able to: Identify linear equations and functions, Write linear equations in standard form and graph them.

Key Words Linear Equations: Has no operations other than addition, subtraction, and multiplication of a variable by a constant. Linear Function: Is a function whose ordered pairs satisfy a linear equation. Standard Form: Ax + By = C

Y-Intercept: The y value when x = 0. X-Intercept: The x value when y = 0.

Example 2-1a State whether is a linear function. Explain. Answer: This is a linear function because it is in the form

Example 2-1b Answer:This is not a linear function because x has an exponent other than 1. State whether is a linear function. Explain.

Example 2-1c State whether is a linear function. Explain. Answer:This is a linear function because it can be written as

Example 2-1d State whether each function is a linear function. Explain. a. b. c. Answer: yes; Answer:No; x has an exponent other than 1. Answer:No; two variables are multiplied together.

Example 2-2a Meteorology The linear function 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 normal body temperature in degrees Fahrenheit? Original function Substitute. Simplify. Answer:Normal body temperature, in degrees Fahrenheit, is 98.6  F.

Example 2-2b 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? Answer: 1.8  F = 1  C Divide 180 Fahrenheit degrees by 100 Celsius degrees.

Example 2-2c Meteorology The linear functioncan be used to find the distance d (s) in miles from a storm, based on the number of seconds s that it takes to hear thunder after seeing lightning. a.If you hear thunder 10 seconds after seeing lightning, how far away is the storm? b.If the storm is 3 miles away, how long will it take to hear thunder after seeing lightning? Answer: 2 miles Answer: 15 seconds

Example 2-3a Writein standard form. Identify A, B, and C. Original equation Subtract 3x from each side. Multiply each side by –1 so that A  0. Answer: and

Example 2-3b Writein standard form. Identify A, B, and C. Original equation Subtract 2y from each side. Multiply each side by –3 so that the coefficients are all integers. Answer: and

Example 2-3c Writein standard form. Identify A, B, and C. Original equation Subtract 4 from each side. Divide each side by 2 so that the coefficients have a GCF of 1. Answer: and

Example 2-3d Write each equation in standard form. Identify A, B, and C. a. b. c. Answer: and Answer:and Answer: and

Example 2-4a Find the x -intercept and the y -intercept of the graph of Then graph the equation. The x -intercept is the value of x when The x -intercept is –2. The graph crosses the x -axis at (–2, 0). Original equation Substitute 0 for y. Add 4 to each side. Divide each side by –2.

Example 2-4b The y -intercept is 4. The graph crosses the y -axis at (0, 4). Likewise, the y -intercept is the value of y when Original equation Substitute 0 for x. Add 4 to each side.

Example 2-4c Use the ordered pairs to graph this equation. Answer:The x -intercept is –2, and the y -intercept is 4. (0, 4) (–2, 0)

Example 2-4d Find the x -intercept and the y -intercept of the graph of Then graph the equation. Answer:The x -intercept is –2, and the y -intercept is 6.

Homework Page 110 (41-46,48-50,54,66,70-72)