### 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.

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.

Write an equation describing the relationship between time and distance.

*d* = 200*t*

**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.

**Solution:**

**Step 1:**

Make a table to relate the number of Hamburgers made, *x*, to the number of buns used, *y*.

**Step 2:**

Graph the ordered pairs on the coordinate plane.

**Step 3:**

Write an equation that describes the relationship.

*y* = 2*x*

Substitute *x* = 5 and solve for *y*.

*y* = 2 × 5

*y* = 10

**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?

**Solution:**

**Step 1:**

Make a table to relate the number of pom-poms sold, *n*, to the amount of money raised, *r*.

**Step 2:**

Graph the ordered pairs on the coordinate plane.

**Step 3:**

Write an equation that describes the relationship.

*r* = 0.41*n*

Substitute *r* = 50 and solve for *n*.

50 = 0.41*n*

50 ÷ 0.41 = 0.41*n* ÷ 0.41

121.95 ≈ *n*

**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?

**Solution:**

**Step 1:**

Make a table to relate the number of weeks, *n*, to the weight, *w*.

**Step 2:**

Graph the ordered pairs on the coordinate plane.

**Step 3:**

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.

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

Name four ordered pairs found on the line plotted using this equation.

Ans:

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.

5. Complete the table and graph to show the relationship between the variables in the equation d= 5 + 5t

d= distance t= time

6. For every hour Sonia worked, she hand-made 2 seashell necklaces for her gift shop.

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.

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.

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.

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.

a. Make a table to represent the data.

b. Write an equation to represent this situation.

**Concept Map**:

### 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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