**Introduction: **

## Dependent variable vs Independent variable:

Dependent variable changes in response to another variable called an independent variable. An independent variable causes a change in a dependent variable. It is independent because its value is not affected by other variables.

For example, a student grade depends on how much he studies. His grade is a dependent variable and the amount of time spent on studying is an independent variable.

**Dependent and independent variables**

**Example 1:**

The distance a car travels, *d*, is dependent on the speed, *s*, at which it travels. Which variable, *d*, distance or *s*, speed is the dependent variable? Explain.

**Solution:**

Speed is the independent variable, and distance is the dependent variable.

In this scenario, the distance, *d*, traveled depends on the speed of the car, *s*, so *d* is the dependent variable.

The speed of the car, *s*, affects the distance traveled, *d*, so *s* is the independent variable.

**Example 2:**

A baker used a certain number of cups of batter, *b*, to make *p* pancakes. Which variable, *p*, pancakes or *b*, batter is the dependent variable? Explain.

**Solution:**

In this scenario, the number of pancakes, *p*, made depends on the number of cups of batter, *b*, so *p* is the dependent variable.

The number of cups of batter used, *b*, affects the number of pancakes made, *p*, so *b* is the independent variable.

**Multiple independent or dependent variables**

**Example 3:**

Annette is preparing for her term-1 examinations. Identify the independent and dependent variables involved in this process.

**Solution:**

**Step 1:**

Identify the variables involved in this scenario.

**Step 2:**

Determine whether the variables are independent or dependent.

**Example 4:**

The Sunryde bike shop rents sports bikes for a day or for a week. What are the independent and dependent variables involved in the cost of rental?

**Solution:**

**Step 1:**

Identify the variables involved in the cost of rental.

**Step 2:**

Determine whether the variables are independent or dependent.

## Exercise:

1. A(n) variable changes in response to another variable.

2. A(n) variable causes the change in a dependent variable.

3. Mike record the number of miles, m, he bikes to help track the number of calories, c, he burns in an hour. Identify the independent and dependent variables involved in this process.

4. Identify the dependent variable and independent variable for the amount of money, m, earned if t raffle tickets are sold.

5. Identify the dependent variable and independent variable for the number of hours, h, worked, and the amount of money, m, earned.

6. Identify the dependent variable and independent variable for the number of shelves, s, in a bookcase and the number of books, b, the bookcase can hold.

7. Identify the dependent variable and independent variable for the number of pages, p, you read in your book in h hours.

8. Name at least two independent variables that could result in a change in a monthly electric bill.

9. Name at least two independent variables that could result in a change in the price of a basket of apples.

10. The cost of a salad at a restaurant depends on many factors. List at least two independent variables that could affect the cost of a salad.

### What have we learned:

• Understanding and identifying dependent and independent variables.

• Identifying multiple independent or dependent variables for the given scenario.

### Concept Map

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