Direct Proportion Direct Proportion Direct Proportion Graphs Direct Proportion formula and calculations Other Direct Proportion formula Inverse Direct Proportion

Direct Proportion Direct Proportion Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT Proportion, if : “ .. When you double the number of cakes you double the cost.” Example : The cost of 6 cakes is £4.20. find the cost of 5 cakes. Cakes Cost Write down two quantities that are in direct proportion. 6  4.20 1  4.20 ÷ 6 = 0.70 5  0.70 x 5 = £3.50

What name do we give to this value Direct Proportion Direct Proportion Example : On holiday I exchanged £30 for $45. How many $ will I get for £50. What name do we give to this value Exchange rate £ $ 30  45 1  45 ÷ 30 = 1.5 50  1.5 x 50 = $75

Direct Proportion Direct Proportion Example : To make scrambled eggs for 2 people we need 2eggs, 4g butter and 40 ml of milk. How much of each for (a) 4 people (b) Just himself (a) Simply multiple by 2 : 4 eggs, 8g butter, 80 ml of milk. (b) Simply half original amounts: 1 eggs, 2g butter, 20 ml of milk.

Direct Proportion Direct Proportion Graphs The table below shows the cost of packets of “Biscuits”. We can construct a graph to represent this data. What type of graph do we expect ?

Direct Proportion Graphs Notice that the points lie on a straight line passing through the origin Direct Proportion Graphs This is true for any two quantities which are in Direct Proportion. 1-Oct-19 Created by Mr. Lafferty Maths Dept.

Direct Proportion KeyPoint Two quantities which are in Direct Proportion Graphs KeyPoint Two quantities which are in Direct Proportion always lie on a straight line passing through the origin.

Direct Proportion X 1 2 3 4 y 6 9 12 Direct Proportion Graphs Example : Plot the points in the table below. Are they in Direct Proportion? X 1 2 3 4 y 6 9 12 We plot the points (1,3) , (2,6) , (3,9) , (4,12)

Direct Proportion Direct Proportion Graphs y 12 Plotting the points (1,3) , (2,6) , (3,9) , (4,12) 11 10 9 8 7 Since we have a straight line passing through the origin x and y are in Direct Proportion. 6 5 4 3 2 1 x 1 2 3 4

Find the formula connecting Direct Proportion Direct Proportion Graphs y 12 Find the formula connecting y and x. 11 10 9 Formula has the form : 8 7 y = kx 6 5 Gradient = 3 4 Formula is : y = 3x 3 2 1 x 1 2 3 4

Direct Proportion Important facts: Direct Proportion Graphs Fill in table Find gradient from graph Write down formula using knowledge from straight line chapter

Direct Proportion Direct Proportion Formula Given that y is directly proportional to x, and when y = 20, x = 4. Find a formula connecting y and x Since y is directly proportional to x the formula is of the form k is the gradient y = kx 20 = k(4) k = 20 ÷ 4 = 5 y = 5x

Direct Proportion Direct Proportion Formula The number of dollars (d) varies directly as the number of £’s (P). You get 3 dollars for £2. Find a formula connecting d and P. Since d is directly proportional to P the formula is of the form k is the gradient d = kP 3 = k(2) k = 3 ÷ 2 = 1.5 d = 1.5P

Direct Proportion Direct Proportion Formula How much will I get for £20 d = 1.5P d = 1.5 x 20 = 30 dollars

Direct Proportion Harder Direct Proportion Formula Given that y is directly proportional to the square of x, and when y = 40, x = 2. Find a formula connecting y and x when . Since y is directly proportional to x squared the formula is of the form y x y = kx2 40 = k(2)2 k = 40 ÷ 4 = 10 y = 10x2

Direct Proportion Harder Direct Proportion Formula Calculate y when x = 5 y = 10x2 y = 10(5)2 = 10 x 25 = 250 y x

Direct Proportion Harder Direct Proportion Formula The cost (C) of producing a football magazine varies as the square root of the number of pages (P). Given 36 pages cost 45p to produce. Find a formula connecting C and P. Since C is directly proportional to “square root of” P the formula is of the form y x k = 48 ÷ 6 = 8

Direct Proportion Harder Direct Proportion Formula How much will 100 pages cost. y x

Inverse Proportion X 1 2 4 8 y 80 40 20 10 Inverse Proportion Inverse Proportion is when one quantity increases and the other decreases. The two quantities are said to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other. Example : Fill in the following table given x and y are inversely proportional. y x X 1 2 4 8 y 80 40 20 10

Inverse Proportion Inverse Proportion Inverse Proportion is the when one quantity increases and the other decreases. The two quantities are said to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other. Example : If it takes 3 men 8 hours to build a wall. How long will it take 4 men. (Less time !!) y x Men Hours 3  8 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours

Inverse Proportion Inverse Proportion Example : It takes 10 men 12 months to build a house. How long should it take 15 men. Men Months 10  12 1  12 x 10 = 120 y x 15  120 ÷ 15 = 8 months

Inverse Proportion Inverse Proportion Example : At 8 m/s a journey takes 32 minutes. How long should it take at 10 m/s. Speed Time 8  32 mins 1  32 x 8 = 256 mins y x 10  256 ÷ 10 = 25.6 mins