Drawing a line (basics)

There are three basic methods that one can use to draw a line in the xy-plane..

1. The table method:
This involves drawing up a table with x and y values.
2. The intercept method:
We find that x- and y-intercepts with this method.
3. The gradient and y-intercept method:
We use the y-intercept and the gradient.

Let's consider an example: y = 2x - 4
Remember the general formula for a line which is y = mx + c. In this case m represents the gradient and c represents the y-intercept.
The y-intercept is where the line intersects the y-axis on the xy-plane.

1. We choose some x values, say -2, -1, 0, 1, 2. We then substitute these values into the equation to obtain the corresponding values of y. We usually do this by drawing up a table to make it easier to see which x and y values correspond.
In our example, if x = 1, then y = -2, so we plot the point (1, -2) on the xy-plane. After plotting a few point you should be able to draw a straight line which goes through all the points.

2. We already know that c represents the y-intercept, which in our case is -4. So we know that (0, -4) is a point on the line. To find the x-intercept we let y = 0, then we find that x = 2. So (2, 0) is also a point on our line. Now we can draw a straight line through these two points and we should obtain the same line as with the first method.

3. We know that the y-intercept is -4. Also, m represents the gradient which is 2. The gradient is also known as the slope and can be found be considering the fraction y/x. So, if y/x = 2, this is the same as saying y/x = 2/1. Hence, we have the point (1,2) on our line, as well as (0,-4). Now we draw the straight line through these points.