#### Introduction:

In this session, we will talk about the graph of proportional relationships. We will see what the graph of a proportional relationship looks like. We will apply the graph to solve problems and answer specific questions.

#### Graph of a Proportional Relationship:

If we trace a proportional relationship on the coordinate plane, we get a straight line that passes through the origin.

If we ever get a graph that is either not a straight line or does not pass through the origin, then the relationship is not a proportional one.

**Example:**

Here, we get a straight line that passes through the origin. Hence, the relationship between the number of t-shirts and the time is a proportional relationship.

#### Interpreting the Graph of a Proportional Relationship:

Once we confirm that the graph represents a proportional relationship, we can use the graph to find key information like the constant of proportionality and the equation representing the proportional relationship and can calculate unknown values.

The constant of proportionality will be the value on the y-axis where the value on the x-axis is 1. Once the constant of proportionality is known, we can use to find the equation of the proportional relationship.

**Example:**

- Does the graph represent a proportional relationship? Explain.
- If yes, what is the constant of proportionality?
- Write an equation to represent the proportional relationship.

Answers:

- As the graph shows a straight line passing through the origin, it represents a proportional relationship.

2. When x=1,y=10. Hence, constant of proportionality is 10.

3. y=10x

#### Exercise:

- Graph the given situation and conclude if it represents a proportional relationship or not. Justify your answer.

x | 2 | 6 | 10 |

y | 15 | 45 | 75 |

2. For the graph obtained in Q1 answer the following questions:

- If it represents a proportional relationship, what is the constant of proportionality?
- What will the value of y for x=8?

#### Concept Summary:

#### What We Have Learned:

- Learning about graphs to recognize a proportional relationship
- Interpreting the graphs of a proportional relationship
- Recognizing graphs of proportional relationships

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