1. Aim: How can we identify linear functions and write linear equations
Aim: How can we identify linear functions and write linear equations? Do Now: Given f(x)=4x2+9, find f(-2) and f(4y)

2. Homework ???s

3. linear relations – relations that have straight line graphs.
linear equation – has no operations other than addition, subtraction, and multiplication of a variable by a constant.
linear function – a function with an ordered pair that satisfy a linear equation.
Vocabulary

4. X-intercept : point where graph crosses x-axis (x,0)
Y-intercept : point where graph crosses y-axis (0,y)
Vocabulary

5. Linear Equations: Nonlinear Equations: 4x-5y=16 2x + 6y2=-25
x=10 (vertical line) y=√x + 2
y=-4 (horizontal line) x + xy = -5/8
f(x)=-2/3x – 1 f(x) = 1/x
y=0.5x xy = 12
Vocabulary

6. Identify Linear Functions
A. State whether g(x) = 2x – 5 is a linear function. Write yes or no. Explain.
Answer: Yes; this is a linear function because it is in the form g(x) = mx + b; m = 2, b = –5.
Example 1A

7. Identify Linear Functions
B. State whether p(x) = x3 + 2 is a linear function. Write yes or no. Explain.
Answer: No; this is not a linear function because x has an exponent other than 1.
Example 1B

8. Is xy = 3 a linear function. Explain.B C D
Example 1C

9. Is 1 + 1 = 3 a linear function. Explain. x yB C D
Example 1C

10. Is f(x) = √3-x a linear function. Explain.B C D
Example 1C

11. f(C) = 1.8C + 32 Original function f(37) = 1.8(37) + 32 Substitute.
Evaluate a Linear Function
A. METEOROLOGY 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?
f(C) = 1.8C + 32 Original function
f(37) = 1.8(37) + 32 Substitute.
= 98.6 Simplify.
Answer: Normal body temperature, in degrees Fahrenheit, is 98.6°F.
Example 2

12. A B C D A. 0.6 second B. 1.67 seconds C. 5 seconds D. 15 seconds
Example 2B

14. Concept

16. Write y = 3x – 9 in standard form.
y = 3x – 9 Original equation
–3x + y = –9 Subtract 3x from each side.
3x – y = 9 Multiply each side by –1 so that A ≥ 0.
Example 3

17. Write 3x + 6y = – 18 in slope-intercept form.
Example 3

18. Write y - 3 = 4(x + 6) in slope-intercept form.
Point -Slope Form
Write y - 3 = 4(x + 6) in slope-intercept form.
Example 3

19. Shareout and Summary: