1. Unit 1 – First-Degree Equations and Inequalities
Chapter 2 – Linear Relations and Functions
2.2 – Linear Equations

2. 2.2 – Linear Equations In this section we will review how to:
Identify linear equations and functions
Write linear equations in standard form and graph them

3. 2.2 – Linear Equations
Linear equation – no other operations other than addition, subtraction, and multiplication of a variable by a constant
x + y = 4
variables cannot be multiplied together
variables cannot appear in a denominator
variables cannot have exponents higher than 1
graph is always a line

4. 2.2 – Linear Equations Linear Equations Not Linear Equations
5x – 3y = 7
x = 9
6s = -3t – 15
y = 1/2x
7a + 4b2 = -8
y = √(x + 5)
x + xy = 1
y = 1/x

5. 2.2 – Linear Equations
Linear function – function whose ordered pairs satisfy a linear equation
f(x) = mx + b where m and b are real numbers

6. 2.2 – Linear Equations Example 1
State whether each function is a linear function. Explain
g(x) = 2x – 5
p(x) = x3 + 2
t(x) = 4 + 7x

7. 2.2 – Linear Equations Example 2
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?
There are 100 Celsius degrees between the freezing and boiling points of water and 180Fahrenheit degrees between these two points. How many Fahrenheit degrees equal 1 Celsius degree?

8. 2.2 – Linear Equations Standard Form Ax + By = C
A, B and C are integers whose greatest common factor is 1
A ≥ 0
A and B are not both zero

9. 2.2 – Linear Equations Example 3
Write each equation in standard form. Identify A, B and C.
y = 3x – 9
-⅔x = 2y – 1

10. 2.2 – Linear Equations
How many points determine a line?
y – intercept – The y-coordinate of the point at which a graph crosses the y-axis
x – intercept – The x-coordinate of the point at which a graph crosses the x-axis

11. 2.2 – Linear Equations Example 4
Find the x-intercept and the y-intercept of the graph of -2x + y – 4 = 0. Then graph the equation.

12. HOMEWORK Page 69 #11 – 17 odd, 18 – 21 all, 23 – 47 odd
2.2 – Linear Equations
HOMEWORK Page 69 #11 – 17 odd, 18 – 21 all, 23 – 47 odd