1. Graphing Linear Equations
From the beginning

2. What is a Linear Equation?y x
A linear equation is an equation whose graph is a LINE.
Not Linear
Linear

3. What is a Linear Equation?y x
The equations we will be graphing have two variables, x and y.
For example,
A solution to the equation is any ordered pair (x, y) that makes the equation true.
The ordered pair (3 , 2) is a solution since,
If we were to plot all these ordered pairs on a graph, we would be graphing a line.

4. Graphing a Linear Equationy x
How do we graph linear equations?
Let’s try this one: y = 3x – 2
Make a Table of values
y = 3(–2) – 2
y = –8 x y –2 –1 1 2
The x - values are picked by YOU! –8
y = 3(–1) – 2
y = –5
Complete the table by inputting the x - values and calculating the corresponding y - values. –5 –2
y = 3(0) – 2
y= –2 1 4
y = 3(1) – 2
y= 1
y = 3(2) – 2
y= 4

5. Graphing a Linear Equationy x
How about another one!
Let’s try y = 5-2x.
First Step:
Make a Table of Values x y –2 –1 1 2 9
Take a moment and complete the chart… 8 5 3 1

6. Graphing Horizontal & Vertical Linesy x
When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example …
Graph x = 3
y = –2
Since there are no y – values in this equation, x is always 3 and y can be any other real number.
Graph y = –2
Since there are no x – values in this equation, y is always – 2 and x can be any other real number.
x = 3