2.1 Defining a straight line

Before we disucss a 'line of best fit', we will first discuss how to define a straight line. Consider the below graph of a straight (linear) line:

When we plot a straight line as we have done above, it can be defined by two things:

  1. The "y-intercept", i.e. the value of y at which the line crosses the y axis. This occurs when x=0
  2. The "slope" of the line. The slope tells us how 'steep' or 'flat' the line is. It also tells us how much y increases (or decreases) for each unit increase in x.

We can write down the equation of a line in a way you may be familiar with:

y=mx+c,

where:

  • m is the slope of the line
  • c is the y-intercept.

By studying the above graph, see if you can answer the following questions:

  1. What is the y-intercept?

The equation of the line is provided in the above graph - you can use this equation to identify the value of c (i.e. the y-intercept).

10

  1. What is the slope?

The equation of the line is provided in the above graph - you can use this equation to identify the value of m (i.e. the slope).

5

  1. What would be the value of y when x=2?

y=5x+10=5×2+10=?

20

0 of 3 correct

To further explain the slope, let's zoom in on the above graph:

Looking at this zoomed in version of the graph, we can see that as we move from the yellow point to the red point, the following happens:

  • x increases by one unit (from 2 to 3)
  • y increases by 5 (from 20 to 25).

No matter where we are on the line, increasing x by one unit will always result in an increase of y by 5, which is the slope.