Graphing Linear Equations

Graphing Linear Equations

• Linear equation: an equation with two variables that are both to the first power.

Ex. x + y = 3

• The graph of a linear equation will always be a straight line.

• Previously, you’ve solved equations that contain just one variable. For example, let’s solve:

2x + 3 = 7

• Linear equations have an infinite number of solutions.

• When we solve a linear equation, we get a list of ordered pairs.

• The graph of all of the ordered pairs creates a straight line.

x + y = 3

x y

Ordered Pairs

Horizontal and Vertical Lines

• Sometimes, the graph of an equation is a horizontal or a vertical line.

• If our equation only contains a “y”, then our graph is a horizontal line.

• If our equation only contains an “x”, then our graph is a vertical line.

Example

y = 3x y

1 3

3 3

-1 3

0.5 3

-3 3

Example

x = 3x y

3 2

3 1

3 -4

3 0.5

3 3

ExamplesFor each of the following linear equations:a) Find four ordered pair that complete the equationb) Plot the ordered pairs on a coordinate plane

1) x + y = 6

2) y = x + 1

3) x = 4

Ordered Pairs

x + y = 6

x y

Ordered Pairs

Y = x + 1

x y

Ordered Pairsx = 2

x y

Slope

• Slope: A number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill.

• Think of a road going uphill (or downhill). The steepness of the road is the slope.

The slope we are studying is associated with the graph of a line.

Steepness

Vertical ChangeHorizontal Change

This ratio is also known asRiseRun

Graph (3,2) and (-1,-1)

Draw a line through the points.

Now that we have our line lets find its slope.

Remember we are finding the following ratio:Vertical or Rise

Horizontal Run

Vertical Changeor the Rise

3

Horizontal Changeor the Run

4

3

Vertical Rise Horizontal Run

34

Find the slope of the following line.

The slope is…

12

Find the slope of the line.

The slope is….

-3

Find the slope of these lines.

The slope is…

• Black line 3

• Red Line 1

• Blue Line -1/2

Find the slope of these lines

The slope is…

• Orange line 0

• Green Line Undefined

• Let’s go back to our first example.• Graph the line that goes through (3,2) and (-1,-1)

Equation

(3,2) and (-1,-1)