A square grid with the following words listed in four quadrants (listed clockwise from top left): Words, Equation, Table, Graph. Arrows point from the Table quadrant to the other three.

In this section we will look at ways to work with a data table.

Isidro is playing a "guess the rule" game on the computer. He types in a number, and the computer gives a number in response. The program generates the following data set:

x y
-6 8
-3 6
0 4
3 2
6 0

What is the change in the y-values from one row to the next row?
Interactive popup. Assistance may be required. Check Your Answer The y-values decrease by 2 for each row. Close Pop Up

What is the change in the x-values from one row to the next row?
Interactive popup. Assistance may be required. Check Your Answer The x-values increase by 3 for each row. Close Pop Up

What is the ratio of the changes in y-values to the changes in x-values?
Interactive popup. Assistance may be required. Check Your Answer - -Two over 3 2 3 Close Pop Up

How does the value of y change as the value of x increases?
Interactive popup. Assistance may be required. Check Your Answer The value of y decreases as the value for x increases. Close Pop Up

Does the value of y decrease at a constant rate or at a variable rate?
Interactive popup. Assistance may be required. Check Your Answer

The value of y decreases at a constant rate. Close Pop Up

How much would the value of y change if the value of x changed by 1?
Interactive popup. Assistance may be required. Check Your Answer The value of y changes by – Two Thirds 2 3 when the value of x increases by 1. Close Pop Up

To calculate the value of y would you multiply the value of x by ( – Two Thirds 2 3 ) or add (– Two Thirds 2 3 ) to the value of x?
Interactive popup. Assistance may be required. Check Your Answer Multiply by – Two Thirds 2 3 Close Pop Up

What is the value of y when the value of x is 0?
Interactive popup. Assistance may be required. Check Your Answer The value of y is 4 when the value of x is 0. Close Pop Up

Use the answer to the previous question to write a new sentence that describes how the value of y relates to the value of x.
Interactive popup. Assistance may be required. Check Your Answer The value of y is 4 more than (– Two Thirds 2 3 ) times the value of x. Close Pop Up

Write your sentence as a mathematical equation.
Interactive popup. Assistance may be required. Check Your Answer y = – Two Thirds 2 3 x + 4 Close Pop Up

Click here if you need a review of plotting points on an axis.

Click here to open a printable sheet of coordinate planes you can use to make draw graphs.

Graph the data from the table on one of the coordinate planes on the sheet you just printed.

x y
-6 8
-3 6
0 4
3 2
6 0

Interactive exercise. Assistance may be required.This activity might not be viewable on your mobile device. If you need help graphing the points from the table above, you can use this plotting applet.

ClickInteractive popup. Assistance may be required.here for applet instructions.

-"screenshot

Source: Simple Plot, Shodor

As you enter data, click the Plot/Update button after each ordered pair to see the data point appear on the graph.

Close Pop Up

ClickInteractive popup. Assistance may be required.here to see the completed graph.

-"" Close Pop Up

If you are drawing a graph to show only the data in the table, you plot individual points on the graph. If you are drawing a graph to represent the relationship between x and y that is shown by your data, then you connect the points with a line that continues on in either direction.

Interactive exercise. Assistance may be required.

Write a verbal description and an equation, and draw a graph that each represent the relationship shown in the following data tables: