Graphing Linear Equations

From the beginning

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What is a Linear Equation?

A linear equation is an equation whose graph is a LINE.

y

x

Linear

Not Linear

( ) ( )2 3 3 2 12+ =

What is a Linear Equation?

A solution to the equation is any ordered pair (x , y) that makes the equation true.

If we were to plot all these ordered pairs on a graph, we would be graphing a line.

The equations we will be graphing have two variables, x and y.

2 3 12x y+ =

y

x

For example,

The ordered pair (3 , 2) is a solution since,

( ) ( )2 0 3 4 12+ =

( ) ( )2 6 3 0 12+ =

( ) ( )2 3 3 6 12- + =

( ) ( )22 1 3 4 123

- + =

The x - values are picked by YOU!

Complete the table by inputting the x - values and calculating the corresponding y - values.

Graphing a Linear Equationy

x

How do we graph linear equations?

Let’s try this one: y = 3x – 2

Make a Table of values

x y

–2

–1

0

1

2

y = 3(–2) – 2 = –8

y = 3(–1) – 2 = –5

y = 3(0) – 2 = –2

y = 3(2) – 2 = 4

y = 3(1) – 2 = 1

–8

–5

–2

1

4

Graphing a Linear Equationy

x

How about another one!

Let’s try x – 2y = 5.

First Step:

Write y as a function of x

x – 2y = 5

–2y = 5 – x

5 12 2

y x

Graphing a Linear Equationy

x

How about another one!

Let’s try x – 2y = 5.

Second Step:

Make a Table of Values

x y

–2

–1

0

1

72

52

–3

5 12 2

y x

–2

Take a moment and complete the chart…

Click the screen when finished

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

Since there are no y – values in this equation, x is always 3 and y can be any other real number.

x = 3

Graph y = –2

Since there are no x – values in this equation, y is always – 2 and x can be any other real number.

y = –2