Key Concepts
• Relate quantities using a table, a graph, and an equation.
• Relate an equation with two operations to a table and a graph.
Introduction:
Analyze the relationship between dependent and independent variables:
You can analyze the relationship between an independent variable and a dependent variable using tables and graphs and relate these to an equation.
Example 1:
The graph shows the distance Marla walked in a certain amount of time.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3490.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3491.png)
Make a table of values for the data in the graph.
Solution:
In this example, time is an independent variable, and distance is a dependent variable.
Make a table of values for the data in the graph.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3491.png)
Write an equation describing the relationship between time and distance.
d = 200t
4.10.1 Relate quantities using a table, a graph, and an equation
Example 2:
At Hamburger Heaven, they use two buns for every hamburger. Find how many buns are required to make 5 hamburgers.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-114.jpeg)
Solution:
Step 1:
Make a table to relate the number of Hamburgers made, x, to the number of buns used, y.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3492-1024x122.png)
Step 2:
Graph the ordered pairs on the coordinate plane.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3493.png)
Step 3:
Write an equation that describes the relationship.
y = 2x
Substitute x = 5 and solve for y.
y = 2 × 5
y = 10
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3492-1024x122.png)
Example 3:
The Transparent Hands Foundation members want to raise $50 to donate to a local charity. They buy pom-poms for $50.55 each. The Transparent Hands Foundation raises $0.41 for each pom-pom they sell.
How many pom poms do they need to sell to reach their fundraising goal of $50?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-115.jpeg)
Solution:
Step 1:
Make a table to relate the number of pom-poms sold, n, to the amount of money raised, r.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3494-1024x466.png)
Step 2:
Graph the ordered pairs on the coordinate plane.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3495-1024x422.png)
Step 3:
Write an equation that describes the relationship.
r = 0.41n
Substitute r = 50 and solve for n.
50 = 0.41n
50 ÷ 0.41 = 0.41n ÷ 0.41
121.95 ≈ n
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3496-1024x565.png)
4.10.2 Relate an equation with two operations to a table and a graph
Example 4:
A puppy weighs 1 pound when it is born and gains 1/2 pound each week. What was the puppy’s weight after 6 weeks?
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-116.jpeg)
Solution:
Step 1:
Make a table to relate the number of weeks, n, to the weight, w.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3497-1024x682.png)
Step 2:
Graph the ordered pairs on the coordinate plane.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3498.png)
Step 3:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3510.png)
Write an equation that describes the relationship.
1/2 n + 1 = w
Substitute n = 6 and solve for w.
1/ 2 × 6 + 1= w
6/2 + 1= w
3 + 1 = w
4 = w
Exercise:
1. How can you analyze the relationship between a dependent and an independent variable using tables, graphs, and equations?
Ans: We can analyze the relationship between an independent variable and a dependent variable using tables and graphs and relate these to an equation.
2. Given below is a graph. Answer the following questions.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3499.png)
a. Who drove the farthest distance?
b. Who drove the fastest?
Ans: a. Monica drove the farthest distance because she travelled 20 miles in 5 hours.
b. Monica drove the fastest because she drove 20 miles, while Dylan drove 10 miles in 5 hours.
3. Complete the following table.
d= distance t = time
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3500.png)
Name four ordered pairs found on the line plotted using this equation.
Ans:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3501.png)
The ordered pairs are (1,4), (2,8), 3,12 , (4,16).
4. Use the graph below and write an equation that represents the relationship between x and y.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3502.png)
5. Complete the table and graph to show the relationship between the variables in the equation d= 5 + 5t
d= distance t= time
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3503.png)
6. For every hour Sonia worked, she hand-made 2 seashell necklaces for her gift shop.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3504.png)
Write an equation that describes the relationship shown in the graph. Also, describe the relationship between the variables in the graph and the equation.
4. The equation c = 2 + 4m can be used to find the c, total cost of a taxi cab ride after in miles.
a. Create a table.
b. Graph it.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3505.png)
5. Ursula is giving her younger sister a bath. The equation g = 2m can be used to find the number of gallons of water in the bathtub after in, minutes.
a. Create a table.
b. Graph it.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3506.png)
6. The Hamburger Hut charges $2.50 for each hamburger. M rs. Shannon’s 6th-grade class will eat lunch at the Hamburger Hut next week.
a. Fill in the table to show the total cost for the number of hamburgers in the table.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3507.png)
b. Write an equation showing the relationship between the total cost and the number of hamburgers.
4. The graph below shows the number of pounds of meat needed to feed a given number of lions in one day.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3508.png)
a. Make a table to represent the data.
b. Write an equation to represent this situation.
Concept Map:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-3509.png)
What have we learned:
• Relate independent variable and dependent variable using a table, a graph, and an equation for the given scenario.
• Relate an equation with two operations to a table and a graph.
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