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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)