Coordinates
This is a way of plotting a point on a graph.
To plot the point A with coordinates (2,3) we start at 0 and move 2 places to the right and 3 places up on the x and y axes.
Example of plotting points: Plot the points A (2,3), B (5,1), C (–3,–2), D (2,–3) and E (–1,2) on the graph below.
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Note: The first number in the bracket indicates the movement right or left.
The second number indicates the movement up or down.
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Graphs (Simple)
The graph of a line can be given in the form of an equation.
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Graphs of straight lines
An example of an equation of a straight line is y = 2x.
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To plot the graph of the equation
We can plot this graph by working out the coordinates. To do this we make up values for x and substitute them into the equation to find the values of y. The results are put in a table, as below.
Table of coordinates for y = 2x
| x |
y |
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| –1 |
–2 |
y = 2 x –1 = –2 |
| 0 |
0 |
y = 2 x 0 = 0 |
| 1 |
2 |
y = 2 x 1 = 2 |
| 3 |
6 |
y = 2 x 3= 6 |
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Plotting these coordinates and drawing a line through them gives the graph of y = 2x below. |
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y = 2x |
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Some simple equations whose lines should be known.
1) y lines are horizontal lines. For example, y = 2, y = –3, y = 0.
2) x lines are vertical lines. For example, x = 5, x =10, x = 0.
3) y = x and y = –x are diagonal lines.
4) x + y lines, for example x + y = 1 passes through 1 on the x axis and 1 on the y axis. |
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| Graphs of x and y lines |
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| Graph of y = x and y = –x |
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| Graph of x + y = 4 and x + y = 1 |
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