Direct Variation. Graph the data is the chart on the next slide. Find the rate of change. April 30, Direct variation lesson.notebook.

Transcription

1 Direct Variation Opener Marshall bought delicious beef biscuits at the bulk food store. The cost was $1.10 for 100 g. Here is a table of costs for different masses. Mass of beef biscuits (g) Costs ($) Graph the data is the chart on the next slide. Find the rate of change. 1

2 The graph is a straight line that passes though. This illustrates. In, we say that the cost varies directly as the mass. When two quantities vary directly they are. The cost is to the mass. Finding the rate of change: The rise is: The run is : The rate of change is. 2

3 Write a Rule: Cost if beef biscuits in $ = (0.011) x (mass of snacks) the rate of change in the mass dollars per gram in grams We can use the rule to determine how much Marshall has to pay for 350 g of beef biscuits. Substitute 350 for the mass of the beef biscuits. Cost of beef biscuits in $ = x 350 = 3.85 The cost of 350 g of beef biscuits is $

4 Now use the rule to determine how much Marshall has to pay for 450 g of beef biscuits. What about if Marshall wanted to buy 800 g of beef biscuits? 4

5 We can use this rule to help us develop an equation for the line. If $ = (0.011) x (mass of biscuits) (where $ represents the y axis, mass of biscuits represents the x axis and the represents the rate of change or slope of the line) Our equation for the line would be: y = 0.011x The equation for any line with direct variation is: y = mx (where m represents the slope of the line) 5

6 The equation for any line with direct variation is: y = mx (where m represents the slope of the line) 6

7 So, direct variation means that the two quantities are proportional and vary directly. When looking at a graph, you can tell it is direct variation because the straight line passes through the origin! Which of these graphs illustrates direct variation? 7

8 Partial Variation Example The cost of pizza with tomato sauce is $9.00. It costs $0.75 for each additional topping. This table shows the cost of a pizza with up to 8 additional toppings. Toppings Costs ($) The cost, in dollars, for a 4 topping pizza is 9+ (4 x 0.75) = Graph the data is the chart on the next slide. Find the rate of change. 8

9 All points make a straight line, but the graph does not passes though. This illustrates. In, we say that the cost of a pizza is the sum of a fixed cost and a variable cost. The point where the line crosses the vertical axis is the. Finding the rate of change: The rise is: The run is : The rate of change is. 9

10 Write a Rule: Cost of pizza in $ = (0.75 X number of toppings) the fixed cost in dollars this is the variable cost in dollars because it depends on the number of toppings. We can use the rule to determine how much someone would have to pay if they ordered a pizza with 12 toppings. Substitute 12 for the number of toppings. Cost of pizza in $ = (0.75 X number of toppings) = (0.75 X 12) = = The cost of ordering a pizza with 12 toppings is $

11 Now use the rule to determine how someone would pay if they ordered a pizza with 15 toppings. Cost of pizza in $ = (0.75 X number of toppings) = (0.75 X 15) = = The cost of a 15 topping pizza would be $ What about if someone ordered a pizza but did not want any toppings? Is the pizza free? Explain your thinking. If the pizza did not have any toppings, it would NOT be free. The $9.00 is a fixed cost, which means that the pizza costs $9.00 initially before they even start adding toppings on. 11

12 We can use this rule to help us develop an equation for the line. If the cost of the pizza is $ = (0.75 X number of toppings) (where $ represents the y axis, number of toppings represents the x axis and the 0.75 represents the rate of change or slope of the line) Our equation for the line would be: y = 0.75x + 9 The equation for any line with direct variation is: y = mx + b (where m represents the slope of the line and b represents the y intercept) 12

13 So, partial variation is when one quantity equals a fixed value plus a constant multiple of another quantity. When looking at a graph, you can tell it is partial variation because the straight line that does not passes through the origin! Which of these graphs illustrates partial variation? Find the equation for each line using the y= mx + b formula. 13

14 Remember, the more work you finish in class, the less homework you will have! 14

15 Remember, the more work you finish in class, the less homework you will have! 15