1. Splash Screen

2. Five-Minute Check (over Lesson 2–1) CCSS Then/Now New Vocabulary
Example 1: Identify Linear Functions
Example 2: Real-World Example: Evaluate a Linear Function
Key Concept: Standard Form of a Linear Equation
Example 3: Standard Form
Example 4: Use Intercepts to Graph a Line
Lesson Menu

3. A. function; one-to-one B. function; onto
Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.
A. function; one-to-one
B. function; onto
C. function; both
D. not a function
5-Minute Check 1

4. A. function; one-to-one B. function; onto
Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.
A. function; one-to-one
B. function; onto
C. function; both
D. not a function
5-Minute Check 1

5. A. function; one-to-one B. function; onto C. function; both
Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.
A. function; one-to-one
B. function; onto
C. function; both
D. not a function
5-Minute Check 2

6. A. function; one-to-one B. function; onto C. function; both
Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither.
A. function; one-to-one
B. function; onto
C. function; both
D. not a function
5-Minute Check 2

7. A. function; one-to-one B. function; onto
Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. {(1, 2), (2, 1), (5, 2), (2, 5)}.
A. function; one-to-one
B. function; onto
C. function; both
D. not a function
5-Minute Check 3

8. A. function; one-to-one B. function; onto
Determine whether the relation is a function. If it is a function, determine if it is one-to-one, onto, both, or neither. {(1, 2), (2, 1), (5, 2), (2, 5)}.
A. function; one-to-one
B. function; onto
C. function; both
D. not a function
5-Minute Check 3

9. Find f(–3) if f(x) = x2 + 3x + 2. A. 20 B. 10 C. 2 D. –2
5-Minute Check 4

10. Find f(–3) if f(x) = x2 + 3x + 2. A. 20 B. 10 C. 2 D. –2
5-Minute Check 4

11. What is the value of f(3a) if f(x) = x2 – 2x + 3?
A. 3a + 3
B. 3a2 – 6a + 3
C. 9a2 – 2a + 3
D. 9a2 – 6a + 3
5-Minute Check 5

12. What is the value of f(3a) if f(x) = x2 – 2x + 3?
A. 3a + 3
B. 3a2 – 6a + 3
C. 9a2 – 2a + 3
D. 9a2 – 6a + 3
5-Minute Check 5

13. Mathematical Practices
Content 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 (algebraically, graphically, numerically in tables, or by verbal descriptions).
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
CCSS

14. You analyzed relations and functions.
Identify linear relations and functions.
Write linear equations in standard form.
Then/Now

15. linear relation nonlinear relation linear equation linear function
standard form
y-intercept
x-intercept
Vocabulary

16. Identify Linear Functions
A. State whether g(x) = 2x – 5 is a linear function. Write yes or no. Explain.
Answer:
Example 1A

17. 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

18. Identify Linear Functions
B. State whether p(x) = x3 + 2 is a linear function. Write yes or no. Explain.
Answer:
Example 1B

19. 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

20. Identify Linear Functions
C. State whether t(x) = 4 + 7x is a linear function. Write yes or no. Explain.
Answer:
Example 1C

21. Identify Linear Functions
C. State whether t(x) = 4 + 7x is a linear function. Write yes or no. Explain.
Answer: Yes; this is a linear function because it can be written as t(x) = mx + b; m = 7, b = 4.
Example 1C

22. A. State whether h(x) = 3x – 2 is a linear function. Explain.
A. yes; m = –2, b = 3
B. yes; m = 3, b = –2
C. No; x has an exponent other than 1.
D. No; there is no slope.
Example 1A

23. A. State whether h(x) = 3x – 2 is a linear function. Explain.
A. yes; m = –2, b = 3
B. yes; m = 3, b = –2
C. No; x has an exponent other than 1.
D. No; there is no slope.
Example 1A

24. B. State whether f(x) = x2 – 4 is a linear function. Explain.
A. yes; m = 1, b = –4
B. yes; m = –4, b = 1
C. No; two variables are multiplied together.
D. No; x has an exponent other than 1.
Example 1B

25. B. State whether f(x) = x2 – 4 is a linear function. Explain.
A. yes; m = 1, b = –4
B. yes; m = –4, b = 1
C. No; two variables are multiplied together.
D. No; x has an exponent other than 1.
Example 1B

26. C. State whether g(x, y) = 3xy is a linear function. Explain.
A. yes; m = 3, b = 1
B. yes; m = 3, b = 0
C. No; two variables are multiplied together.
D. No; x has an exponent other than 1.
Example 1C

27. C. State whether g(x, y) = 3xy is a linear function. Explain.
A. yes; m = 3, b = 1
B. yes; m = 3, b = 0
C. No; two variables are multiplied together.
D. No; x has an exponent other than 1.
Example 1C

28. 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:
Example 2

29. 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

30. Divide 180 Fahrenheit degrees by 100 Celsius degrees.
Evaluate a Linear Function
B. 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.
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?
Divide 180 Fahrenheit degrees by 100 Celsius degrees.
Answer:
Example 2

31. Divide 180 Fahrenheit degrees by 100 Celsius degrees.
Evaluate a Linear Function
B. 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.
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?
Divide 180 Fahrenheit degrees by 100 Celsius degrees.
Answer: 1.8°F = 1°C
Example 2

32. A. 50 miles
B. 5 miles
C. 2 miles
D. 0.5 miles
Example 2A

33. A. 50 miles
B. 5 miles
C. 2 miles
D. 0.5 miles
Example 2A

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

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

36. Concept

37. Write y = 3x – 9 in standard form. Identify A, B, and C.
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.
Answer:
Example 3

38. Write y = 3x – 9 in standard form. Identify A, B, and C.
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.
Answer: 3x – y = 9; A = 3, B = –1, and C = 9
Example 3

39. Write y = –2x + 5 in standard form.
A. y = –2x + 5
B. –5 = –2x + y
C. 2x + y = 5
D. –2x – 5 = –y
Example 3

40. Write y = –2x + 5 in standard form.
A. y = –2x + 5
B. –5 = –2x + y
C. 2x + y = 5
D. –2x – 5 = –y
Example 3

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

42. Likewise, the y-intercept is the value of y when x = 0.
Use Intercepts to Graph a Line
Likewise, the y-intercept is the value of y when x = 0.
–2x + y – 4 = 0 Original equation
–2(0) + y – 4 = 0 Substitute 0 for x.
y = 4 Add 4 to each side.
The y-intercept is 4. The graph crosses the y-axis at (0, 4).
Example 4

43. Use the ordered pairs to graph this equation.
Use Intercepts to Graph a Line
Use the ordered pairs to graph this equation.
Answer:
Example 4

44. Use the ordered pairs to graph this equation.
Use Intercepts to Graph a Line
Use the ordered pairs to graph this equation.
Answer: The x-intercept is –2, and the y-intercept is 4.
Example 4

45. A. x-intercept = –2 y-intercept = 6
What are the x-intercept and the y-intercept of the graph of 3x – y + 6 = 0?
A. x-intercept = –2 y-intercept = 6
B. x-intercept = 6 y-intercept = –2
C. x-intercept = 2 y-intercept = –6
D. x-intercept = –6 y-intercept = 2
Example 4

46. A. x-intercept = –2 y-intercept = 6
What are the x-intercept and the y-intercept of the graph of 3x – y + 6 = 0?
A. x-intercept = –2 y-intercept = 6
B. x-intercept = 6 y-intercept = –2
C. x-intercept = 2 y-intercept = –6
D. x-intercept = –6 y-intercept = 2
Example 4

47. End of the Lesson