Identifying and Representing Proportional Relationships

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Presentation transcript:

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 Determine the constant of proportionality. Hours Worked (x) 1 2 3 4 Total Earnings (y) $7.50 $15.00 $22.50 $30

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

Finding the Constant of Proportionality Ex. 3 Determine the constant of proportionality. Cookies (x) 2 3 4 5 Price (y) $1.00 $1.50 $2.00 $2.50

Finding the Constant of Proportionality Ex. 4 Determine the constant of proportionality. People (x) 5 6 7 8 Slices of Pizza (y) 17.5 21 24.5 28

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

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

Proportional or Not? Is the table above showing a proportional relationship? If it is, what is the constant of proportionality. Input (x) 2 3 4 5 Output (y) 3.5 5.25 7 8.75

Proportional or Not? Is the table above showing a proportional relationship? If it is, what is the constant of proportionality. Input (x) 1 2 3 4 Output (y) 6.3 12.6 18.6 25.2

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

Finding the Constant of Proportionality on a Graph Find the y value for x = 1.

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

Graph and find k. Input (x) 1 2 3 4 Output (y) 1.5 4.5 6

Determining Proportional Relationships by the Equations Must be in the format y = kx ProportionalNot Proportional y = 7x y = x - 4 y = 1 3 x y = 2x – 3 What do you notice?

Determining Proportional Relationships by the Equations Must be in the format y = kx y = 5x YES y = x – 2 NO y = 1 2 x YES y = -9x YES y = 3x – 4 NO