# Equations and graphs

Consider this table of values of and .

0 | 20 |

1 | 30 |

2 | 40 |

3 | 50 |

Notice that for every increase of in the the increases by . This constant difference shows that there is a linear relationship between and . If we plot the values on the axes we get the straight line in the graph above.

### Gradient

The gradient of the line is . The gradient of any line can be calculated using the formula rise over run (either by reading off the graph or using any two coordinates from the table).

*e.g. *Point 1: $latex(1,30)$ and Point 2:

## Straight line equations

The general form of a straight line is

Where is the gradient of the line and is the intercept (i.e. where the line crosses the axis).

This form is handy for sketching a line and for reading off the gradient.

*e.g.* Sketch the line* *

The and the

Note that sometimes we need to rearrange an equation into the form .

* e.g.* Find the gradient and y intercept of the line

The line will cut the axis at with a gradient of .

Use the desmos online calculator to draw different straight lines to understand the relationship between the equation and the graph.

### Special graphs

### Horizontal lines

Line:

Gradient = 0

### Vertical Lines

Line:

Gradient = undefined

### Parallel Lines

Lines: and

The gradient of parallel lines are equal.

## Tables and graphs activity

Complete the following interactive activity

## Further information

- Press the Printer Friendly button at the top left-hand corner to download a printable handout
- Kahn academy uses video to explain another worked example of drawing a line with slope and intercept and a set of practice problems that you can use to review your understanding.