Year 10 Interactive Maths - Second Edition

## Equation of a Straight Line

To establish a rule for the equation of a straight line, consider the previous example.

An increase in distance by 1 km results in an increase in cost of \$3. We say that the rate of change of cost with respect to distance is \$3 per kilometre.

The information given in the graph can be represented by the equation c = 5 + 3d.  That is:

###### In general:

A line with equation y = mx + c has gradient m and y-intercept c.

The gradient of a straight line is the coefficient of x.

###### Particular Case

If a straight line passes through the origin, then its y-intercept is 0.  So, the equation of a straight line passing through the origin is

y = mx

where m is the gradient of the line.

#### Example 8

Write down the equation of the straight line that has m = 5 and c = 3.

##### Solution:

#### Example 9

Calculate the gradient of the straight line given in the following diagram; and find its equation.

#### Example 10

Find the equation of the line joining the points (2, 3) and (4,7).