Key Concepts
- Find a pattern to write an equation.
- Make and analyze a table to write an equation.
Introduction:
Use pattern to write an equation:
You can use patterns in a table to write an equation that relates the independent and dependent variables.
Example 1:
Use the pattern in the table below to write an equation.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3581.png)
Solution:
In the above table, the dependent variable m is 3 times the independent variable j.
Hence, the equation is m = 3j.
4.9.1 Find a pattern to write an equation
Example 2:
The table shows the number of yards, y, that a professional rides in s seconds. Find a pattern that relates the variables. If the cyclist maintains this speed, how far would the cyclist ride in 8 seconds?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3582.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3584.png)
Solution:
Step 1:
Look for a pattern in the table that relates y, the dependent variable and s, the independent variable.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3583.png)
Step 2:
Write an equation to describe the relationship.
12.2 times the value of s = the value of y
12.2s = y
Or
y = 12.2s
Step 3:
Find the distance covered in 8 seconds.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3766.png)
y = 12.2s
y = 12.2(8)
y = 97.6
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3582.png)
Example 3:
The table below shows how many candles are in different numbers of boxes. Find a pattern that explains the relationship between the values of c and b. Use words and numbers to describe the pattern. How many candles will there be in 10 boxes?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3583.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3590.png)
Solution:
Step 1:
Look for a pattern in the table that relates c, the dependent variable and b, the independent variable.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3585.png)
Step 2:
Write an equation to describe the relationship.
4 times the value of b = the value of c
4b = c
Or
c = 4b
Step 3:
Find the number of candles in 10 boxes.
c = 4b
c = 4(10)
c = 40
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3585.png)
4.9.2 Make and analyze a table to write an equation
Example 4:
Kayla owes her mother $70. She repays her mother an amount of $5 each week. How much will Kayla owe her mother after 12 weeks?
![Example 4](https://www.turito.com/learn-internal/wp-content/uploads/2022/10/Example-4.png)
Solution:
Make a table and look for a pattern that relates the variables.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3586.png)
Write an equation to describe the relationship.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3587-1024x540.png)
Find how much Kayla will owe after 12 weeks.
a = 70 – 5w
a = 70 – 5(12)
a = 70 – 60
a = 10
Example 5:
Lauren went to a pizza shop to eat a small pizza. She read the menu as follows,
The cost of small pizza is $6.
Each topping costs $2.
Help Lauren in finding the total cost of a pizza with 6 toppings.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3591.png)
Solution:
Make a table and look for a pattern that relates the variables.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3589.png)
Write an equation to describe the relationship.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3588-1024x534.png)
Find the total cost of a pizza with 6 toppings.
c = 6 + 2t
c = 6 + 2(6)
c = 6 + 12
c = 18
Exercise:
1. Use the pattern in the table below to write an equation.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5850.png)
2. Use the equation y = 2x – 7 to complete the following table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5851.png)
3. Write a rule and an equation that represents the pattern in the following table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5852.png)
4. Write a rule and an equation that represents the pattern in the following table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5853.png)
5. The table shows Brenda’s age, b, when Talia’s age, t, is 7, 9, and 10. Find the pattern and then write a rule and an equation that represents the pattern. Then find Brenda’s age when Talia is 12.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5854.png)
6. Write a rule and an equation that represents the pattern in the following table. Then complete the table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5855.png)
7. Write a rule and an equation that represents the pattern in the following table. Then complete the table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5856.png)
8. Write an equation that best describes the pattern in the following table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5857.png)
9. Write an equation that best describes the pattern in the following table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5858.png)
10. Use the equation t = 5d + 5 to complete the following table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5859.png)
What have we learned:
- Find a pattern in a table that relates the dependent and independent variable and write an equation.
- Make a table, look for a pattern and write an equation.
Concept map:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3596-1024x446.png)
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