ALGEBRA

Graphs

Graphs

Co-ordinates

algebraIn your exam you should definitely expect graph questions. There are a number of skills you should learn to help you to tackle these more easily, starting with co-ordinates.

Co-ordinates are two numbers which correspond to where a point should be placed on a graph.

They always come in pairs: one number for the horizontal x axis and the other for the vertical y axis.

For example, here is a co-ordinate: (3, 8).

The number on the left, 3, tells you how many units you should go across the x axis. Is the number is positive you go right, if it’s negative you go left.

The number on the right, 8, tells you how many units you should go along the y axis. If the number is positive you go up, if it’s negative you go down.

For instance, for the coordinate (-3, 5) you would go 3 left on the x axis and five up on the y axis.

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Straight-line graphs

mathsA straight-line graph, as the name suggests, produces a straight line.

The equation for a straight line graph will contain at least two of the following terms:

  • – an x term
  • – a y term
  • – a number

For example, all the following are straight line graph equations:

  • x = y
  • x = 3
  • y = 2x -4
  • 6x + y = 6

In an exam, you might be asked to complete a table then plot the points onto a graph.

If you’re asked to draw a graph using an equation then always figure out the points on a table first so that you can plot them. Figure out at least three values so you can easily see if you go wrong.

For example, plot the following equation: y = x + 2

First, draw up a table:

x -4 -2 0 2 4
y = x + 2 -2 0 2 4 6

Now you have 5 points: (-4, -2), (-2, 0), (0, 2), (2, 4) and (4, 6)

You can now plot these onto a graph.

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The gradient

mathsThe gradient refers to how steep a line is. You might be asked to figure out the gradient of a straight line in your exam.

To find the gradient:

  • – pick two points on the line
  • – using a ruler draw a line down from the higher point on the line and across from the lower part of the line to form a right-angled triangle.
  • – using the same given on the graph, count how many units make up the vertical length of the triangle and then the horizontal length.

Put these values into the following calculation to figure out the gradient:

vertical length horizontal length

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Curved graphs

Drawing a curved graph uses the same principals as drawing a straight line graph: you need to substitute numbers into the equation to calculate points which you can then plot onto a graph.

The equation for a curved graph comes in the format:

y = ax2+b

For example: complete the table for y = x2 + 5 then plot the graph.

x 0 1 2 3 4 5
y = x2 + 5

Substitute the values give for x into the equation:

For instance, for x = 0: y = 02 + 5 = 5

x 0 1 2 3 4 5
y = x2 + 5 5 6 9 14 21 30

Now you have the following points to plot on your graph: (0, 5), (1, 6), (2, 9), (3, 14) and (5, 30).

You’ll know if you have the correct points because when you join up the points you should get a curved line.

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Real life models

A graph is a good way of visually interpreting a formula.

It also provides a fuller set of information than a few points alone.

In your exam you might be asked to interpret a graph or take information from it.