## Finding Lines using y-y1=m(x-x1)

A useful way of finding the equation of a line is to use the formula , where m is the gradient of the line and and are taken from the given point

### Finding the equation of the line given the gradient and a point

- Get the values of , ,
- Substitute into the formula
- Rearrange the formula to the desired form

Example

Find the line with a gradient of -2 that passes through the point

So , ,

### Finding the equation of the line given a parallel line and a point

- Use the gradient of the parallel line for m
- Get the values of and from the given point
- Substitute into the formula
- Rearrange the formula to the desired form

Example

Find the equation of the line which is parallel to and passes through the point

So , ,

### Finding the equation of the line given a perpendicular line and a point

- Get the gradient of the perpendicular line and use the negative reciprocal for m
- Get the values of and from the given point
- Substitute into the formula
- Rearrange the formula to the desired form

Example

Find the equation of the line which is perpendicular to and passes through the point

The gradient of the given line is -4, so the perpendicular gradient is

From the point and

### Finding the equation of the line given two points

- Find the gradient from the points using or
- Use either point in the formula, your choice
- Rearrange the formula to the desired form

Example

Find the line which passes through the points and

m = gradient =

I will use the point , because both values are positive, but remember you would get the same result if you used

and

So substituting gives

### Finding the equation of the Perpendicular bisector between two points

- Find the gradient between the points and use the negative reciprocal for m
- Find the mid-point between the two points and use this for and
- Substitute into the formula
- Rearrange the formula to the desired form

Example

Find the perpendicular bisector between the points and

Gradient between the points is

The mid-point if

and

So substituting gives