Algebra
Drawing graphs
To draw the graph of a straight line:
- Make a table
- Write down the coordinates of points on the line
- Use suitable axes to plot your points, then draw your line
Example
1. Draw the graph of \(y = 2x + 1\)
| \(x\) | -2 | -1 | 0 | 1 | 2 |
| working | \(2 \times ( - 2) + 1\) | \(2 \times ( - 1) + 1\) | \(2 \times ( 0) + 1\) | \(2 \times ( 1) + 1\) | \(2 \times ( 2) + 1\) |
| \(y\) | -3 | -1 | 1 | 3 | 5 |
| \(x\) |
|---|
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| working |
|---|
| \(2 \times ( - 2) + 1\) |
| \(2 \times ( - 1) + 1\) |
| \(2 \times ( 0) + 1\) |
| \(2 \times ( 1) + 1\) |
| \(2 \times ( 2) + 1\) |
| \(y\) |
|---|
| -3 |
| -1 |
| 1 |
| 3 |
| 5 |
2. Coordinates are: (-2, -3), (-1, -1), (0, 1), (1, 3) and (2, 5)
3.
Question
Draw the straight line with equation \(y = 3x - 2\)
| \(x\) | -2 | -1 | 0 | 1 | 2 |
| working | \(3 \times ( - 2) - 2\) | \(3 \times ( - 1) - 2\) | \(3 \times ( 0) - 2\) | \(3 \times ( 1) - 2\) | \(3 \times ( 2) - 2\) |
| \(y\) | -8 | -5 | -2 | 1 | 4 |
| \(x\) |
|---|
| -2 |
| -1 |
| 0 |
| 1 |
| 2 |
| working |
|---|
| \(3 \times ( - 2) - 2\) |
| \(3 \times ( - 1) - 2\) |
| \(3 \times ( 0) - 2\) |
| \(3 \times ( 1) - 2\) |
| \(3 \times ( 2) - 2\) |
| \(y\) |
|---|
| -8 |
| -5 |
| -2 |
| 1 |
| 4 |
Coordinates: (-2, -8), (-1, -5), (0, -2), (1, 1) and (2, 4)
Special lines
Parallel lines have the same gradient
Vertical lines have a gradient which is undefined
Equation \(x = a\)
Horizontal lines have a gradient of zero
Equation \(y = b\)
