U4 L6 5.1 Direct Variation & 5.2 Partial Variation (Spring 2017) (completed).notebook April 11, 2017

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1 Apr 11-10:24 AM 1

2 ACTIVITY: Crazy Taxi Watch the following video. What is the queson being asked? Apr 6-8:03 AM 2

3 EXTENSION QUESTIONS: a) How much would the trip cost if you traveled 25 km? b) How far would the taxi take you for $75? c) Assume that the taxi company changer their fees so that the taxi meter begins at $4 and adds an addional $2.50 per kilometre travelled. i) How would this change the graph? ii) How would this change the equaon? Apr 6-8:45 AM 3

4 Graphing & Analytic Geometry Day 6: Direct & Partial Variation Learning Goal: Students can 1) compare the proper es of direct & par al varia on 2) iden fy the ini al value Apr 11-5:03 PM 4

5 CONSOLIDATE our understanding: A relaonship between two variables in which one variable is a constant mulple of the other (i.e. y = mx); its graph is a straight line thatpasses through the origin. What does that mean (in English please...)? In terms of an equation... A direct variaon has an equaon of the form y=mx where the ini al value is 0 and m represents the rate of change OR slope. In terms of a graph... The graph of a direct variaon is a straight line that passes through the origin. In terms of a table... Both x and y values go up by a constant amount, and when x = 0, y = 0. x y Apr 11-5:14 PM 5

6 A relaonship between two variables in which the dependent variable is the sum of a constant number and a constant mulple of the independent variable (i.e. y = mx +b); its graph is a straight line that does NOT pass through the origin. What does that mean (in English please...)? In terms of an equation... A paral variaon has an equaon of the form y=mx+b where b represents theini al valueand m represents the rate of change OR slope. In terms of a graph... The graph of a paral variaon is a straight line that does NOT pass through the origin. In terms of a table... Both x and y values go up by a constant amount, and when x = 0, y equals any number other than 0. x y Apr 11-5:16 PM 6

7 EX. 1. Michael works as a salesman in an electronics store. For each month his fixed earnings are $2000. His variable earnings are 15% of all his sales. Write an equaon that represents Michael's monthly earnings. STEP 1: Idenfy the inial value (will not change) Fixed quanty (this will be the "b" in the equaon y=mx+b) = STEP 2: Idenfy the variable part (the part that changes) Variable quanty (this will be the "m" in the equaon y=mx+b) = STEP 3:Put it all together by placing the numbers for m and b into the equaon. b) Is this an example of direct or paral variaon? Apr 11-5:37 PM 7

8 EX. 2. Jenny has a part-me job babysi<ng for her neighbours. If she charges $12 per hour, write an equaon represenng how much Jenny makes. STEP 1: Idenfy the inial value (will not change) Fixed quanty (this will be the "b" in the equaon y=mx+b) = STEP 2: Idenfy the variable part (the part that changes) Variable quanty (this will be the "m" in the equaon y=mx+b) = STEP 3:Put it all together by placing the numbers for m and b into the equaon. b) Is this an example of direct or paral variaon? Apr 11-5:42 PM 8

9 SUMMARY: Compare Direct and Par al varia on rela ons Apr 8-10:07 AM 9

10 Practice:1) pg. 242 #1, 3, 5, 13 2)pg. 250 C1 #1, 2, 7, 10 Apr 8-10:07 AM 10