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# Graphs of Linear Equations

## Graph lines presented in ax+by = c form

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Using Tables to Graph Functions
License: CC BY-NC 3.0

#### Example 2

For the following linear function written in function form, complete the table of values and plot the graph.

 -3 -13 -1 -7 1 -1 3 5 5 11

First, use the equation to calculate the output values ‘.’

Repeat the process to calculate the values for the variable ‘.’

Write the calculated ‘’ values in the table.

Plot the ordered pairs on the Cartesian grid and join the plotted points with a smooth, straight line.

License: CC BY-NC 3.0

#### Example 3

For the following linear function create a table of values and plot the points to draw the graph:

First, use the equation to calculate the output values ‘.’

Repeat the process to calculate the values for the variable ‘.’

Write the calculated ‘’ values in the table.

 -2 -7 -1 -5 0 -3 1 -1 2 1

Plot the ordered pairs on the Cartesian grid and join the plotted points with a smooth, straight line.

License: CC BY-NC 3.0

#### Example 4

Plot the graph of the line having  as its equation.

First, remember this is the graph of one of the special lines.

Next, describe what the graph will look like.

A vertical line passing through the point  and parallel to the -axis.

Then, graph the line on the Cartesian grid.

License: CC BY-NC 3.0

#### Example 5

Plot the graph of the line having  as its equation.

First, remember this is the graph of one of the special lines.

Next, describe what the graph will look like.

A horizontal line passing through the point  and parallel to the -axis.

Then, graph the line on the Cartesian grid.

License: CC BY-NC 3.0

### Review

Create a table of values for each equation and then graph it on the coordinate plane.

To see the Review answers, open this PDF file and look for section 9.5.

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### Vocabulary Language: English

Cartesian Plane

The Cartesian plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin.

Function

A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.

linear equation

A linear equation is an equation between two variables that produces a straight line when graphed.

Slope

Slope is a measure of the steepness of a line. A line can have positive, negative, zero (horizontal), or undefined (vertical) slope. The slope of a line can be found by calculating “rise over run” or “the change in the $y$ over the change in the $x$.” The symbol for slope is $m$

Standard Form

The standard form of a line is $Ax + By = C$, where $A, B,$ and $C$ are real numbers.

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