Quiz #11 - Identifying Proportional Relations | PDF Math Study Guide

Quiz #11 - Study Guide Identifying Proportional Relations From Equations All Proportional Relationships Take On The Equational Form of: ​ ​ ​ ​ ​ ​ ​ ​ Equation Proportional or Not...

Quiz #11 - Study Guide Identifying Proportional Relations From Equations All Proportional Relationships Take On The Equational Form of: ​ ​ ​ ​ ​ ​ ​ ​ Equation Proportional or Not Proportional ​ Proportional ​ Proportional Not Proportional Not Proportional Proportional Relationship From A Graph ​ ​ ​ ​ All MUST Be True: 1)​ Straight Line 2)​ Go Through Origin (0, 0) Proportional​ ​ ​Not Proportional Straight Line​ ​ ​Straight Line ​ ​ ​ ​ &​ ​ ​ BUT Goes Through​​ ​DOES NOT Go Through Origin (0,0)​ ​ ​Origin (0, 0)  Quiz #11 - Study Guide Finding The Constant of Proportionality Reading A Graph Ordered Pairs ​ ​ ​ (x , y) (2, 10) → Gets plotted on a graph. Where 2 on the x-axis and 5 on the y-axis meet When x is 1, y is the constant. ​ ​ ​ (1, k) ​ ​ ​ (1, 5) → k = 5 EXAMPLE #1 Plot the following points on the coordinate plane: (0, 10) , (1, 8) , (2, 6) , (3, 4) , (4, 2) Is this a proportional relationship? ​ No, it is a straight line, but it ​ ​ does not go through ​ ​ the origin (0, 0) EXAMPLE #2 There is a proportional relationship between the number of months a person has had a streaming service subscription and the total amount of money they have paid for the subscription. After 6 months, a user has paid $ 47.94. The point (6, 47.94) is shown in the graph. What is the constant of proportionality in this relationship? ​ (1, k) -> (1, 10) -> k = 10 What does the constant of proportionality mean in this situation? ​ For every month of streaming service it costs $10. Write an equation that represents the relationship between C , the total cost of the subscription, and m , the number of months. ​ y = 10x​ ​ ​ Let y = Cost (c) ​ Let x = Time (t)​ ​ c = 10t  Quiz #11 - Study Guide Determine the coordinates of three more points on this line and label them on the graph. ​ c = 10t​​ ​ Let t = 2​ ​ Let t = 8​ ​ Let t = 14 ​ ​ ​ ​ c = 10(2)​ ​ c = 10(8)​ ​ c = 10(14)​ ​ ​ ​ ​ ​ c = 20​ ​ ​ c = 80​ ​ ​ c = 140 ​ ​ ​ ​ (2, 20)​ ​ ​ (8, 80)​ ​ ​ (14, 140) What does the point (8, 80) mean in this situation on the graph? It cost $80 for 8 months of streaming service EXAMPLE #3 Mia and Jamal bike home from school at a steady pace. Mia bikes 1.25 kilometers and it takes her 4 minutes. Jamal bikes 1.75 kilometers and it takes him 7 minutes. Graph two lines that represent Jamal’s and Mia’s bike rides. ​ Mia (4, 1.25) ​ Jamal (7, 1.75) This is proportional, therefore point (0, 0) can be used for both For each line, find each value of k.Then plot and label the point (1, k). ​ ​ Mia​ Using point (4, 1.25) on the graph ​ ​ ​ (1, 0.31) ​ ​ Jamal Using point (7, 1.75) on the graph ​ ​ ​ (1, 0.25) Who bikes faster? Mia ​ Reading Graph -> Go to any time on the x-axis and follow it up. Mia will go farther in any given amount of time than Jamal Looking At Constants -> (Mia) 0.31 > 0.25 (Jamal) ​ ​ ​ ​ Mia’s constant is greater than Jamal’s