## Gradients and Equations of Lines

The general equation of a line may be wriiten as (1) where m is the gradient and is the – intercept, or where is again the gradient.

Find the equation of the line which passes through the two points and we have to find the gradient We can then use either equation (1) in which case we have to solve for by putting on of the two points in the question into the line. Suppose we pick the first point,  so the equation of the line is (1)

If we are also asked to express the equation of the line in the form we can multiply (1) by 3 to clear the fractions: then subtract from both sides to give: To use the equation we find the gradient as above then choose one of the points and substitute it into the equation as For example, suppose we choose the first point above: Then add 5 to both sides to obtain We can also rearrange this into the form as above.

We may also have to find the equation of a line from a graph. The method is shown below. We use the equation We can read the intercept off the graph. It is 2. We find the gradient using The most obvious points to pick for and are where the graph crosses the coordinate axes. These are the points and The gradient is The equation of the line is then  