Identifying and Representing Proportional Relationships Discovering Proportional Relationships

Identifying and Representing Proportional Relationships

Discovering Proportional Relationships • A giant tortoise moves at a slow but steady pace. It takes the giant tortoise 3 seconds to travel 10. 5 inches. – How far does the tortoise travel in 1 second? – Suppose the tortoise travels 12 seconds. How could you find the distance the tortoise travels?

Important Terms • Rate of Change: is a rate that describes how one quantity changes in relation to another quantity. • Proportional Relationship: a relationship in which the rate of change is constant.

Important Terms • Proportion: a statement that two rates or ratios are equivalent. • Constant of Proportionality (k): The ratio of the two quantities or y=kx – Must be multiplied by a constant amount to get your output.

Finding the Constant of Proportionality • To find k you must divide the y value by the x value.

Finding the Constant of Proportionality Ex. 1 Hours Worked (x) 1 2 3 4 Total Earnings (y) $7. 50 $15. 00 $22. 50 $30 • Determine the constant of proportionality.

Finding the Constant of Proportionality Ex. 2 People (x) 3 5 7 9 Slices of Pizza (y) 9 15 21 27 • Determine the constant of proportionality.

Finding the Constant of Proportionality Ex. 3 Cookies (x) 2 3 4 5 Price (y) $1. 00 $1. 50 $2. 00 $2. 50 • Determine the constant of proportionality.

Finding the Constant of Proportionality Ex. 4 People (x) 5 6 7 8 Slices of Pizza (y) 17. 5 21 24. 5 28 • Determine the constant of proportionality.

Proportional or Not? Input (x) 1 2 3 4 Output (y) 2 4 6 8 • Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.

Proportional or Not? Input (x) 3 4 5 6 Output (y) 18 24 30 34 • Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.

Proportional or Not? Input (x) 2 3 4 5 Output (y) 3. 5 5. 25 7 8. 75 • Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.

Proportional or Not? Input (x) 1 2 3 4 Output (y) 6. 3 12. 6 18. 6 25. 2 • Is the table above showing a proportional relationship? If it is, what is the constant of proportionality.

Proportional or Not? - Graphs • Two conditions: –Must pass through the origin –Must be a straight line

Finding the Constant of Proportionality on a Graph 30 25 20 15 10 5 0 0 1 2 Find the y value for x = 1. 3 4 5 6

Which of the following graphs show direct variation (proportional relationship)?

Graph and find k. Input (x) 1 2 3 4 Output (y) 1. 5 3 4. 5 6

Determining Proportional Relationships by the Equations •

Determining Proportional Relationships by the Equations •