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

Given an equation, you can generate a graph, fill in values for a table, and write a description.

Sydney finds that the data from her science experiment can be represented by the equation listed below.

y = 3x – 1

Answer the following questions to write a verbal description for the equation.
If you are given a value for x, what two steps do you need to follow to calculate a value for y?
Interactive popup. Assistance may be required. Check Your Answer Step 1: Multiply x by three.
Step 2: Subtract one from that product. Close Pop Up

Re-write your answer to the previous question in one complete sentence. (It is often helpful to start with the phrase, "The value of y is...")
Interactive popup. Assistance may be required. Check Your Answer The value of y is one less than three times the value of x. Close Pop Up

Use the following questions to help you fill in the table below.
Calculate the value for y if x = -2
Interactive popup. Assistance may be required. Hint
y = 3(-2) – 1 Close Pop Up Interactive popup. Assistance may be required. Check Your Answer y = -7 Close Pop Up

Calculate the value for y if x = -1
Interactive popup. Assistance may be required. Hint
y = 3(-1) – 1 Close Pop Up Interactive popup. Assistance may be required. Check Your Answer y = -4 Close Pop Up

Calculate the value for y if x = 0
Interactive popup. Assistance may be required. Hint
y = 3(0) – 1 Close Pop Up Interactive popup. Assistance may be required. Check Your Answer y = -1 Close Pop Up

Calculate the value for y if x = 1
Interactive popup. Assistance may be required. Hint
y = 3(1) – 1 Close Pop Up Interactive popup. Assistance may be required. Check Your Answer y = 2 Close Pop Up

Calculate the value for y if x = 2
Interactive popup. Assistance may be required. Hint
y = 3(2) – 1 Close Pop Up Interactive popup. Assistance may be required. Check Your Answer y = 5 Close Pop Up

Copy the following table into your notes and, based on your answers to the previous questions, fill in the missing values.

x process y
-2    
-1    
0    
1    
2    
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Click here to see the completed table.
x process y
-2 y = 3(-2) – 1 -7
-1 y = 3(-1) – 1 -4
0 y = 3(0) – 1 -1
1 y = 3(1) – 1 2
2 y = 3(2) – 1 5
Close Pop Up

Now that you have a table of values, use what you learned in section 3 to draw a graph of the relationship.

Interactive popup. Assistance may be required.

Click here to see a completed graph.

 graph of a line that slopes up and crosses the y axis at -1 Close Pop Up

Create a verbal description, a table, and a graph to represent the relationship shown in the following equation.

y = Three Fourths 3 4 x + 2
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Hint

 Pick x values for your table that are evenly divisible by 4. Close Pop Up Interactive popup. Assistance may be required.

Check Your Answers

 Verbal description:
The value of y is two more than Three Fourths 3 4 times the value of x

Table:
x y
-8 -4
-4 -1
0 2
4 5
8 8


Graph:
graph of a line that slopes up and crosses the y axis at 2 Close Pop Up