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

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

Direct Proportion £$ Example :On holiday I exchanged £30 for $45. How many $ will I get for £  45 1  45 ÷ 3 0 =  1.5 x 50 = $75 What name do we give to this value Exchang e rate

Direct Proportion (a)Simply multiple by 2 : 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 4 eggs, 8g butter, 80 ml of milk. (b)Simply half original amounts: 1 eggs, 2g butter, 20 ml of milk.

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

14-Aug-15Created by Mr. Lafferty Maths Dept. Direct Proportion Graphs Notice that the points lie on a straight line passing through the origin This is true for any two quantities which are in Direct Proportion.

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

Direct Proportion Example : Plot the points in the table below. Are they in Direct Proportion? Direct Proportion Graphs We plot the points (1,3), (2,6), (3,9), (4,12)X1234y36912

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

1 Direct Proportion Find the formula connecting y and x. Direct Proportion Graphs Formula has the form : x y Gradient = 3 Formula is :y = 3x y = kx

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

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

Direct Proportion Q. 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. Direct Proportion Formula Since d is directly proportional to P the formula is of the form d = kP k is the gradient 3 = k(2) k = 3 ÷ 2 = 1.5 d = 1.5P

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

Direct Proportion Q. 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 = kx 2 40 = k(2) 2 k = 40 ÷ 4 = 10 y = 10x 2 Harder Direct Proportion Formula y x

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

Direct Proportion Q. 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 k = 48 ÷ 6 = 8 Harder Direct Proportion Formula y x

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

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. Inverse ProportionX1248y y x

MenHours 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 !!) 3  8 1  3 x 8 = 24 hours 4  24 ÷ 4 = 6 hours Inverse Proportion y x

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

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