### Let’s Think About It

The students of the local high school are selling potted plants to raise funds for their soccer team to buy new uniforms. Each six-pack of potted plants will sell for $6.50. A new sports store has agreed to match the money raised by the students as a donation to the team. The money raised by the students will be displayed on a poster-size Cartesian graph and presented to the sports store. How can the students create such a graph?

In this concept, you will learn to use tables to graph functions.

### Guidance

Consider the following Cartesian graph that represents the equation

The equation function form and can be used to create a table of values that will make the statement of equality true. Remember an equation written in function form can be used to determine values for the output ‘

Using

-4 | -8 |

-2 | -2 |

0 | 4 |

2 | 10 |

4 | 16 |

Use this process to calculate the values of the output variable for each of the given input values.

The input value associated with the corresponding output value can be written as an ordered pair

The ordered pairs are plotted on the Cartesian graph and are shown as red points. These points were then joined by a smooth straight line to draw the graph. The graph is a straight line such that the equation that produced this line was a **linear function**. The highest exponent of the variables of a linear function is one.

There are two special linear functions that produce a straight line graph. One of the straight lines is a vertical line that is parallel to the -axis and the other is a horizontal line that is parallel to the -axis.

Let’s graph each of these special lines.

A line having

A line having

as its equation will pass through the point such that it will be parallel to the -axis.

### Guided Practice

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.

### Examples

#### Example 1

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.

#### Example 2

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

Then, graph the line on the Cartesian grid.

#### Example 3

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.

### Follow Up

Remember the plotted plants and the soccer uniforms?

The students need to create a poster size graph to show how much money was raised. How can the students create this graph?

They can create a table of values and plot the ordered pairs from the table.

First, write an equation in function form to represent the sale of potted plants.

Let

represent the money raises and let represent the number of potted plants sold.\begin{align*}y=6.50x\end{align*}

Next, create a table of values and use the equation expressed in function form to calculate the output value for each input value.

50 | |

100 | |

150 | |

200 | |

250 |

\begin{align*} \begin{array}{rcl} x&=&50\\ y&=&6.50x\\ y&=&6.50(50) \qquad \text{Substitute } x=50 \text{ into the equation}. \\ y&=&\$325.00 \qquad \ \text{Perform the multiplication to clear the parenthesis}. \end{array}\end{align*}

Repeat the same process for the remaining input values.

\begin{align*}\begin{array}{rcl} x&=&100\\ y&=&6.50x\\ y&=&6.50(100)\\ y&=&\$650.00 \end{array}\end{align*}

\begin{align*}\begin{array}{rcl} x&=&150\\ y&=&6.50x\\ y&=&6.50(150)\\ y&=&\$975.00 \end{array}\end{align*}

\begin{align*}\begin{array}{rcl} x&=&200\\ y&=&6.50x\\ y&=&6.50(200)\\ y&=&\$1300.00 \end{array}\end{align*}

\begin{align*}\begin{array}{rcl} x&=&250\\ y&=&6.50x\\ y&=&6.50(250)\\ y&=&\$1625.00 \end{array}\end{align*}

Next, write the calculated ‘

’ values in the table.50 | 325 |

100 | 650 |

150 | 975 |

200 | 1300 |

250 | 1625 |

Then, plot the ordered pairs shown in the table on a Cartesian grid.

The sports store will have to match the $1,625.00 raised by the students.

### Video Review

https://www.youtube.com/watch?v=2-dUHLHeyTY

### Explore More

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