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Unformatted text preview: CHAPTER 2 Lines and Graphs Almost everything in this chapter is revision from GCSE maths. It re minds you how to draw graphs, and focuses in particular on straight line graphs and their gradients . We also look at graphs of quadratic functions, and use graphs to solve equations and inequalities. An im portant economic application of straight line graphs is budget con straints . — ./ — 1. The Gradient of a Line A is a point with coordinates (2 , 1); B has coordinates (6 , 4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x y 1 2 3 4 5 61 1 2 3 4 51 A B 4 3 When you move from A to B , the change in the xcoordinate is Δ x = 6 2 = 4 and the change in the ycoordinate is Δ y = 4 1 = 3 The gradient (or slope) of AB is Δ y divided by Δ x : Gradient = Δ y Δ x = 3 4 = 0 . 75 (The symbol Δ, pronounced “delta”, denotes “change in”.) It doesn’t matter which end of the line you start. If you move from B to A , the changes are negative, but the gradient is the same: Δ x = 2 6 = 4 and Δ y = 1 4 = 3, so the gradient is ( 3) / ( 4) = 0 . 75. There is a general formula: The gradient of the line joining ( x 1 ,y 1 ) and ( x 2 ,y 2 ) is: Δ y Δ x = y 2 y 1 x 2 x 1 23 24 2. LINES AND GRAPHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x y 1 2 3 4 5 61 1 2 3 4 51 C D 2 4 Here the gradient is negative. When you move from C to D : Δ x = 4 2 = 2 Δ y = 1 5 = 4 The gradient of CD is: Δ y Δ x = 4 2 = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x y a b c d In this diagram the gradient of line a is positive, and the gradient of b is negative: as you move in the xdirection, a goes uphill, but b goes downhill. The gradient of c is zero. As you move along the line the change in the ycoordinate is zero: Δ y = 0 The gradient of d is infinite. As you move along the line the change in the xcoordinate is zero (so if you tried to calculate the gradient you would be dividing by zero). Exercises 2.1 : Gradients (1) (1) Plot the points A (1 , 2) ,B (7 , 10) ,C ( 4 , 14) ,D (9 , 2) and E ( 4 , 1) on a diagram. (2) Find the gradients of the lines AB,AC,CE,AD . 2. LINES AND GRAPHS 25 2. Drawing Graphs The equation y = 0 . 5 x +1 expresses a relationship between 2 quantities x and y (or a formula for y in terms of x ) that can be represented as a graph in x y space. To draw the graph, calculate y for a range of values of x , then plot the points and join them with a curve or line....
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This note was uploaded on 04/12/2010 for the course ECON DEAM taught by Professor Vines during the Spring '10 term at Oxford University.
 Spring '10
 Vines
 Economics

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