1. Chapter 2 Examples Section 2 Linear Functions

2. Objective: Students will identify patterns with linear forms of equations and functions. They will also manipulate linear functions to display them in Standard Form and identify the x and y intercepts.

3. Notes Linear Equation: 1.Equation with no operators other than addition, subtraction, and multiplication of a variable by a constant. 2.Variables cannot be multiplied together. 3.Degree (highest power of any variable in the equation) of equation is not bigger than one.

4. Notes Linear Function: A function whose ordered pairs satisfy a linear equation.

5. Notes Standard Form: Ax + By = C 1.A must be greater than zero. 2.A and B can’t both be zero. 3.A, B, and C must be integers. 4.x and y must be on same side. x - y intercepts: Used in Standard Form to graph linear functions. x - intercept: (x, 0) set y = 0 and solve for x. y - intercept: (0, y) set x = 0 and solve for y.

6. Example 1 ❖ State whether each function is a linear function. ❖ A.) g(x) = 2x – 5. ❖ B.) p(x) = x 3 + 2. ❖ C.) g(x) = 4 + 7x.

7. Example 2 ❖ Meteorology ❖ The linear function f(C) = (9/5)C + 32 can be used to find the number of degrees Fahrenheit, f, that are equivalent to a degree number Celsius, C. ❖ On the Celsius scale, normal body temperature is 37 ◦ C. What is the normal body temperature in degrees Fahrenheit? ❖ Solve the function f(C) for C so you can find the function that changes degrees Fahrenheit to Celsius.

8. Example 3 ❖ Write each equation in Standard Form. Then identify A, B, and C. ❖ y = 3x – 9. ❖ -(2/3)x = 2y – 1. ❖ 8x - 6y + 4 = 0.

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

10. Homework Pg. 66 15-24 all, 28-50 even, 53-55 all