Report

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 Total Earnings (y) $7.50 $15.00 $22.50 $30 3 4 • 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 • Must be in the format y = kx ProportionalNot Proportional y = 7x y=x-4 y= 1 x 3 What do you notice? y = 2x – 3 Determining Proportional Relationships by the Equations • Must be in the format y = kx 1. y = 5x 2. y = x – 2 3. y = 1 x 2 4. y = -9x 5. y = 3x – 4 YES NO YES YES NO