Algebra 2

Chapter 2.2 Linear Relations & Functions

Target Goals:1. Identify linear relations and functions2. Determine the intercepts of linear equations/functions3. Graph linear equations/functions using intercepts

New Vocabulary• Linear Relations– Relations with straight lines when graphed

• Linear Equation– Has no operations except addition, subtraction, &

multiplication of a variable by a constant– Fractions of numbers are ok, but variable can NOT be

in the denominator!– No exponents on variables other than 1 (which usually

is not written)

Linear vs. Non-LinearLinear Equations Non-Linear Equations

4 5 16x y 24 5 16x y

10x 2y x 2

13

y x

3

1y

x

5

8x xy

Function Notation vs. Equations

• f(x) = y • f(x) replaces the dependent variable (y)

y = 2x + 1 f(x) = 2x + 1

Characteristics of Linear Functions

• Graph is a straight line• Only operations seen are +, -, or multiplication

of variable and a constant (a number)• No variables in the denominator• Exponents on variables are only 1• No variables are multiplied together

Practice: State whether each function is a linear function. Write yes or no and explain your answer.

3 1Ex 1) ( )

2 3g x x

5Ex 2) ( )

4f x

x

3Ex 3) ( ) 2p x x

Yes!!

No – variable in the denominator

No – exponent on variable is not 1

Connection to Order of Operations/Formulas/Real-Life!

• Ex 4) 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 it in degrees Fahrenheit?

( ) 1.8 32f C C

( ) 1.8 32f C C (37) 1.8 37 32f

(37) 66.6 32f (37) 98.6 Ff

INTERCEPTS

• y-intercept: the point where the line crosses the y-axis; (0, b)

• x-intercept: the point where the line crosses the x-axis; (a, 0)

Practice: Find the x-intercept and the y-intercept of the graph of the linear equation. Then graph the equation.Ex 5) 2x + 5y – 10 = 0

x-intercept

2x + 5y – 10 = 02x + 5(0) – 10 = 02x – 10 = 02x = 10x = 5

(5, 0)

y-intercept

2x + 5y – 10 = 02(0) + 5y – 10 = 05y – 10 = 05y = 10y = 2

(0, 2)

Practice: Find the x-intercept and the y-intercept of the graph of the linear equation. Then graph the equation.Ex 6) -2x + y – 4 = 0

x-intercept

-2x + y – 4 = 0-2x + (0) – 4 = 0-2x – 4 = 0-2x = 4x = -2

(-2, 0)

y-intercept

-2x + y – 4 = 0-2(0) + y – 4 = 0y – 4 = 0y = 4

(0, 4)