Algebra 2
Chapter 2.2
Linear Relations & Functions
Target Goals:
1. Identify linear relations and functions
2. Determine the intercepts of linear
equations/functions
3. 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-Linear
Linear Equations
Non-Linear Equations
44xx55yy2 16
16
y x x10
2
23
yy x  1
3x  1
5
x  xy  
8
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
1
Ex 1) g ( x)   x 
2
3
Yes!!
5
Ex 2) f ( x) 
x4
No – variable in the
denominator
Ex 3) p( x)  x3  2
No – exponent on
variable is not 1
Connection to Order of
Operations/Formulas/Real-Life!
• Ex 4) 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
f (37)  1.8 37   32
f (37)  66.6  32
f (37)  98.6F
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 yintercept of the graph of the linear equation.
Then graph the equation.
Ex 5) 2x + 5y – 10 = 0
x-intercept
y-intercept
2x + 5y – 10 = 0
2x + 5(0) – 10 = 0
2x – 10 = 0
2x = 10
x=5
2x + 5y – 10 = 0
2(0) + 5y – 10 = 0
5y – 10 = 0
5y = 10
y=2
(5, 0)
(0, 2)
Practice: Find the x-intercept and the yintercept of the graph of the linear equation.
Then graph the equation.
Ex 6) -2x + y – 4 = 0
x-intercept
y-intercept
-2x + y – 4 = 0
-2x + (0) – 4 = 0
-2x – 4 = 0
-2x = 4
x = -2
-2x + y – 4 = 0
-2(0) + y – 4 = 0
y–4=0
y=4
(-2, 0)
(0, 4)