3.1 Understanding what graphs tell us  (Page 3/5)

The first number in the brackets always refers to the numbers on the x–axis, and the second number refers to the number on the y–axis.

• Let us play follow–the–leader. On the diagram alongside, (–3 ; 5) is marked with a white circle. From there the arrow points to (0 ; 2). The ne x t arrow leads to (4½ ; 2½) and then to (3 ; 0), (–5 ; –3), (1 ; –6), (0 ; 0), (–4 ; 1½) and (–4½ ; 4½), ending at the black circle.

Make sure that your understand how coordinates work before you continue.

The axes (the dark lines) divide the Cartesian plane into four quadrants.

2.1 Write down the coordinates of the cros---sings marked A to G on the dia­gram. Use brackets and semicolons and put the two numbers in the correct order.

2.2 Find the following dots on the dia­gram and carefully join them in order. What does your picture remind you of?

(–4 ; 0) (–4 ; –6) (–3 ; –6) (–3 ; –2) (–2 ; –2)(–2 ; –6) (–1 ; –6) (–1 ; –2) (3 ; –2) (3 ; –6)(5 ; –6) (5 ; 0) (7 ; 0) (7 ; 2) (5½ ; 2)(4½ ; 4) (4 ; 2) (–4 ; 2) (–6 ; 4) (–4 ; 0)

• René Descartes (pronounced daycar ) was born in France in 1596, and died of pneumonia when he was 54. At the time he lived, there were many wars in Europe and he became a soldier and took part in several campaigns. He was not only a mathematician, but also studied physics (particularly optics), astronomy, meteorology and anatomy as well as the theory of music. While working on some difficult mathematical problems, he developed the system of numbering graph paper so that geometry could be combined with algebra to solve the problems. This is why the design of the diagram above is called the Cartes ian plane.

ACTIVITY 3

To use a table of values to draw a graph on the Cartesian plane

[LO 1.3, 2.1, 2.2, 2.5]

1 In this table there is a relationship between a number in the top row of the table (input value) and the one directly below it (output value). There are some missing numbers and these gaps have been labelled a , b and c .

1.1 Study the first seven columns of numbers in the table until you can see the pattern, and write down the rule used to calculate the output value from the input value. Now use this rule to fill in the gaps by calculating what a , b and c have to be if they follow the same rule.

1.2 We now take the pairs of numbers in each column to make up sets of coordinates. They always look like this:

(input value ; output value),

with the input value in the first position.

• Here are the first two sets of co-ordinates: ( 1 ; 17 ) and ( 2 ; 22). Write down the rest in the same way, including the last three with your calculated values instead of a , b and c .

1.3 Make a dot on this Cartesian plane for every set of coordinates you have found from the table.

You should have ten dots, and they should lie in a straight line.

Use a ruler to draw the line.

2 The next table shows the charges for a gardener who charges R35 per hour or part–hour.

2.1 Write down your explanation of the fact that there are two R70’s in the second row, and also two R105’s.