The most important calculation we need to do when dealing with straight line equations is to calculate the gradient. This is a measure of how steep the line is. If the line is going upwards it will be positive, and if it is going downwards it will be negative. It can be less than 1 (a gradient of 1 means it is at an angle of 45 degrees.

We calculate the gradient using the following formula:

Let’s plot the line y=2x+1 and try calculating the gradient for it. Does it matter how big a triangle we draw?

Exercise

Let’s complete exercise 14D on page 225 of the textbook:

The answers are below:

We don’t really need to draw the line to find the gradient. Because of how it is calculated, as long as we know two points on the line, we can just go ahead and use the formula, the same as we would do if we had the graph in front of us:

Let’s try this (without drawing a graph) for two examples:

1.) Find the gradient of the line joining the points (1,3) and (5,11)

2.) Find the gradient of the line joining the points (1,5) and (5,3)

Exercise

Let’s complete exercise 14E on page 226 of the textbook:

The answers are below: