Creating a Table of Values
For each situation in numbers 1 – 3, create a table of values with at least five columns to represent the situation.
Julio works at a clothing store and makes $14 per hour.
Compare your answer:
Number of hours | 0 | 1 | 2 | 3 | 4 | 5 |
Amount earned | 0 | 14 | 28 | 42 | 56 | 70 |
Jake had cavities at his last dentist visit. The dentist told him to brush his teeth for two minutes each time he brushes.
Compare your answer:
Amount earned | 1 | 2 | 3 | 4 | 5 |
Total number of minutes brushed | 2 | 4 | 6 | 8 | 10 |
For a fundraiser, Celia ran 5 miles on Monday (day 0) and then 3 miles every day after that.
Compare your answer:
0 | 1 | 2 | 3 | 4 | 5 | |
5 | 8 | 11 | 14 | 17 | 20 |
Using a Table of Values to Write Equations
Table of values can be used to write equations. The tables from Creating a Table of Values all represent linear equations.
For 4 - 8, revisit the table from question 1 and write an equation to represent the table of values. Notice that columns for the and values are added.
0 | 1 | 2 | 3 | 4 | 5 | |
0 | 14 | 28 | 42 | 56 | 70 |
What is the starting value (when , what does equal)?
How would you describe this value on the graph?
Compare your answer:
-intercept
What is the rate of change, or the change between the -values over the change between the -values?
Compare your answer:
or 14
How would you describe this value on the graph?
Compare your answer:
slope
Using the information in questions 4 – 7, what would the equation be for the values represented by the table? Use slope-intercept form.
Compare your answer:
or
Write an equation from the table of values created in question 2 of Creating a Table of Values.
Hint: (Work backward to find the value where using the pattern set in the table of values).
0 | 1 | 2 | 3 | 4 | 5 | |
? | 2 | 4 | 6 | 8 | 10 |
Compare your answer:
(note: subtract the top row by 1 and the bottom row by 2 to go back to where for the -intercept).
Write an equation from the table of values created in question 3 of Creating a Table of Values
0 | 1 | 2 | 3 | 4 | 5 | |
? | 2 | 4 | 6 | 8 | 10 |
Compare your answer:
Video: Writing an Equation from a Table of Values
Watch the following video to learn more about writing equations from a table of values.
Create Your Own Situation
Think of your own situation that could be modeled by a linear equation. Create a table of values that represents that situation. Write your problem down then switch with a partner. Make a table of values for each other’s problems. Then, check your work together.
Next, plot the points of each table of values in a coordinate plane. Answer the questions after discussing with your partner:
Describe the scenario created by your partner.
Compare your answer:
Answers vary.
Use Desmos to graph the table of values to represent your partner’s scenario.
Use the graphing tool or technology outside the course. Graph the equation that represents this scenario using the Desmos tool below.
Compare your answer:
Answers vary.
Does your partner’s data model a linear relationship or not? Describe how you determined your answer.
Compare your answer:
The points form a line. This happens because the same number was added to each value in the top row and the same number was added to each value in the bottom row of the tables.
Are you ready for more?
Extending Your Thinking
Kylie pays $20 to rent a scooter plus $0.40 per mile she drives the scooter. Create a table of values to represent Kylie’s situation starting with .
Compare your answer:
0 | 1 | 2 | 3 | 4 | 5 |
20 | 20.40 | 20.80 | 21.20 | 21.60 | 22.10 |
Use the table to determine how much she has to pay after 5 miles.
Compare your answer:
Kylie would pay $22.10.
Self Check
Additional Resources
Writing Linear Equations from Tables
When writing linear equations from tables, it is important to identify the slope and the -intercepts from the table.
Example
Given the table, write an equation in slope-intercept form.
0 | 1 | 2 | 3 | 4 | |
12 | 16 | 20 | 24 | 28 |
Step 1 - Identify the -intercept.
The -intercept is the starting value, when .
Looking at the table, when , the -value is 12, so this is the -intercept.
Step 2 - Identify the slope.
Slope is the change in over the change in .
The -values change by 4 each time. The -values change by 1 each time.
The slope is or 4.
Step 3 - Write the equation in slope-intercept form.
Slope intercept form is , where is the slope and is the -intercept.
Substitute the values, .
Try it
Try It: Writing Linear Equations from Tables
Given the table, write an equation in slope-intercept form.
0 | 1 | 2 | 3 | |
6 | 11 | 16 | 21 |
Compare your answer:
Here is how to write the equation in slope-intercept form:
Step 1 - Identify the -intercept.
The -intercept is the starting value, when .
Looking at the table, when , the -value is 6, so this is the -intercept.
Step 2 - Identify the slope.
Slope is the change in over the change in .
The -values change by 5 each time.
The -values change by 1 each time. The slope is or 5.
Step 3 - Write the equation in slope-intercept form.
Slope intercept form is , where is the slope and is the -intercept.
Substitute the values, .