www mathsrevision com Direct Proportion Graphs Direct Proportion

www. mathsrevision. com Direct Proportion Graphs Direct Proportion formula and calculations Other Direct Proportion formula Inverse Direct Proportion 10/28/2020 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com 9 8 6 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Learning Intention 1. To explain the term Direct Proportion. Success Criteria 1. Understand the idea of Direct Proportion. 2. Solve simple Direct Proportional problems. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com 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 6 4. 20 Write down two quantities that are 1 4. 20 ÷ 6 = 0. 70 in direct proportion. 10/28/2020 5 Created by Mr. Lafferty Maths Dept. 0. 70 x 5 = £ 3. 50

Direct Proportion www. mathsrevision. com Direct Proportion Example : On holiday I exchanged £ 30 for $45. How many $ will I get for £ 50. £ 10/28/2020 $ 30 1 50 45 45 ÷ 30 = 1. 5 What name do we give to this Exchange value rate 1. 5 x 50 = $75 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Example : (a) To make scrambled eggs for 2 people we need 2 eggs, 4 g butter and 40 ml of milk. How much of each for (a) 4 people (b) Just himself Simply multiple by 2 : 4 eggs, 8 g butter, 80 ml of milk. (b) Simply half original amounts: 1 eggs, 2 g butter, 20 ml of milk. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Now try Exercise 1 Ch 8 (page 101) 10/28/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Graphs Learning Intention 1. To explain how Direct Proportion Graph is always a straight line. 10/28/2020 Success Criteria 1. Understand that Direct Proportion Graph is a straight line. 2. Construct Direct Proportion Graphs. Created by Mr. Lafferty Maths Dept.

Direct Proportion Graphs www. mathsrevision. com 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 ? 10/28/2020 Created by Mr. Lafferty Maths Dept.

Notice that the Direct Proportion Graphs points lie on a straight line passing through the origin This is true for any two quantities which are in Direct Proportion. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Graphs Key. Point Two quantities which are in Direct Proportion always lie on a straight line passing through the origin. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion Graphs www. mathsrevision. com Example : Plot the points in the table below. Are they in Direct Proportion? X y 1 3 2 6 3 9 4 12 We plot the points (1, 3) , (2, 6) , (3, 9) , (4, 12) 10/28/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Direct Proportion Graphs y 12 Plotting the points 11 10 (1, 3) , (2, 6) , (3, 9) , (4, 12) 9 8 7 Since we have a straight line 6 passing through the origin 5 x and y are in 4 Direct Proportion. 3 2 1 10/28/2020 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4 x

www. mathsrevision. com Direct Proportion Graphs y 12 Find the formula connecting 11 y and x. 10 9 8 Formula has the form : 7 y = kx 6 5 Gradient = 3 4 Formula is : y = 3 x 3 2 1 10/28/2020 Created by Mr. Lafferty Maths Dept. 0 1 2 3 4 x

Direct Proportion www. mathsrevision. com Direct Proportion Graphs Key point of Ex 2 Fill in table Find gradient from graph Write down formula using knowledge from straight line chapter 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Now try Exercise 2 Ch 8 (page 104) 10/28/2020 Created by Mr. Lafferty Maths Dept.

Starter Questions www. mathsrevision. com 9 8 6 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Formula Learning Intention 1. To explain how to work out Direct Proportion formula. Success Criteria 1. Understand the process for calculating direct proportion formula. 2. Calculate gradient from information given. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion Formula www. mathsrevision. com Q. 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 y = kx 20 = k(4) k = 20 ÷ 4 = 5 y = 5 x 10/28/2020 Created by Mr. Lafferty Maths Dept. k is the gradient

Direct Proportion Formula www. mathsrevision. com 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. Since d is directly proportional to P the formula is of the form d = k. P 3 = k(2) k = 3 ÷ 2 = 1. 5 d = 1. 5 P 10/28/2020 Created by Mr. Lafferty Maths Dept. k is the gradient

Direct Proportion Formula www. mathsrevision. com Q. How much will I get for £ 20 d = 1. 5 P d = 1. 5 x 20 = 30 dollars 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Direct Proportion Formula Exercise 3 Ch 8 (page 105) 10/28/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Harder Direct Proportion Formula Learning Intention 1. To explain how to work out harder Direct Proportion formula. Success Criteria 1. Understand the process for calculating direct proportion formula. 2. Calculate k for harder direct proportion formula. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion Harder Direct Proportion Formula www. mathsrevision. com Q. y 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 x 40 = k(2)2 k = 40 ÷ 4 = 10 y = 10 x 2 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion Harder Direct Proportion Formula www. mathsrevision. com Q. Calculate y when x = 5 y = 10 x 2 y = 10(5)2 = 10 x 25 = 250 y x 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion Harder Direct Proportion Formula www. mathsrevision. com Q. The cost (C) of producing a football magazine varies as the square root of the number of pages (P). Given 36 pages cost 45 p 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 10/28/2020 k = 48 ÷ 6 = 8 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Harder Direct Proportion Formula Q. How much will 100 pages cost. y x 10/28/2020 Created by Mr. Lafferty Maths Dept.

Direct Proportion www. mathsrevision. com Harder Direct Proportion Formula Exercise 4 B Ch 8 (page 106) 10/28/2020 Created by Mr. Lafferty Maths Dept.

www. mathsrevision. com Starter Questions 10/28/2020 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www. mathsrevision. com Inverse Proportion Learning Intention 1. To explain the term Inverse Proportion. Success Criteria 1. Understand the idea of Inverse Proportion. 2. Solve simple inverse Proportion problems. 10/28/2020 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www. mathsrevision. com 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 : y x 10/28/2020 Fill in the following table given x and y are inversely proportional. X 1 2 4 8 y 80 40 20 10 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www. mathsrevision. com 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 : y x 10/28/2020 If it takes 3 men 8 hours to build a wall. How long will it take 4 men. (Less time !!) Men 3 1 4 Created by Mr. Lafferty Maths Dept. Hours 8 3 x 8 = 24 hours 24 ÷ 4 = 6 hours

Inverse Proportion www. mathsrevision. com Inverse Proportion Example : It takes 10 men 12 months to build a house. How long should it take 15 men. Men 10 1 15 y Months 12 12 x 10 = 120 ÷ 15 = 8 months x 10/28/2020 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www. mathsrevision. com Inverse Proportion Example : At 8 m/s a journey takes 32 minutes. How long should it take at 10 m/s. Speed 8 1 10 y Time 32 mins 32 x 8 = 256 mins 256 ÷ 10 = 25. 6 mins x 10/28/2020 Created by Mr. Lafferty Maths Dept.

Inverse Proportion www. mathsrevision. com Inverse Proportion Exercise 5 Ch 8 (page 108) 10/28/2020 Created by Mr. Lafferty Maths Dept.