Welcome to this lesson on the Equation of a Line.

By the end of this lesson you will be able to:

	Find the equation of the line linking any two points
	Use the equation of the line to find
(i) The slope of the line   (ii) The points that are on that line   (iii) Where the line cuts the 'x' and 'y' axes   (iv) The intersection of any two lines
	Draw any line from the equation of the line.

Find the equation of the line linking the two points (3, 0) and (0, -1).

Steps to answering this question:

Find slope of line between two points.

Using this slope (called m) and one of the points find the equation of the line.

Using the formula:

y - y = m(x - x)

Note: The m in this formula is the slope

The equation of the line is:

x - 3y = 3

We will now look at how we can effectively use this equation of the line to give us more information about the line and the points on it.

This information includes:

1. Slope

2. Verifying that a point belongs to a line

3. Where the line cuts the x and y axes.

4. Intersection of two lines.

Slope

We have already covered how to calculate the slope when given two points.

Sometimes you won't be given that information - instead you will be given the equation of the line, so you need to be able to calculate the slope from this.

The main way of calculating the slope when given the equation of the line is to:

Rewrite the equation of the line in the following form:

y = mx + c

where m, the co-efficient of x, gives you the slope.

Example 1.

Find the slope of the line

x + y - 2 = 0

Example 2.

Find the slope of the line

7x + 5y -11 = 0.

Example 3.

Find the slope of the line,

-x - 2y - 4 = 0.

Verifying that a point belongs to a line.

To see if a point is on a particular line, we do the following:

If the equation is not satisfied, the point is not on the line.

Example 4.

Is (4, 1) on the line x + y = 5.

First of all, we label the point.

Substitute the x and y values into the equation of the line.

If the equation is satisfied, the point is (4, 1) on the line.

Example 5.

Is (-1, 3) on the line 2x + 3y = 10.

Find where the line cuts the x and y axes.

This information is useful in graphing lines.

Firstly, where does the line cross the x axis?

Now, where does the line cross the y axis?

Where does the line 3x - 5y = 9 cross the x axis?

Where does the line 2x + y = 7 cross the y axis?

Intersection of two lines

This type of question involves a simultaneous equation.

Example 6.

Find the point of intersection between the following two lines:

L: x + y = 5

K: 2x - y = 4.

Draw the line 2x + y - 8 = 0

First of all, find two points on the line.

The easiest ones to find are where the line crosses the x and y axes.

Now plot the two points.

This lesson has covered:

	Finding the equation of the line linking any two points
	Using the equation of the line to find
(i) The slope of the line   (ii) The points thats are on that line   (iii) Where the line cuts the 'x' and 'y' axes   (iv) The intersection of any two lines
	Drawing any line from the equation of the line.
	Types of questions asked on this topic.