We have seen in a previous post the gradient of a straight line graph. Today we are going so have a look at the y-intercept.
Now as you know a graph is composed of two axes. The y-axis and the x-axis as shown in fig 1.
Now in order to find the y-intercept you will need a straight line that passes through the y-axis, i.e it intercept the y-axis, as seen in fig 2 below.
As you can see in fig 2 above all three lines crosses the y-axis. As a result the three lines would have a y-intercept.
How to obtain the y-intercept of a straight line?
1. If the x-axis starts at 0
As you can see in fig 3 below the point at which the line crosses the y-axis is at the y=2 coordinate. Hence the y-intercept is 2.
We can thus define the y-intercept as being the value of the y-coordinate when the x-coordinate is 0.
2. If the x-axis does not start at 0
As you can see in fig 4 below the x-axis does not start at 0. Hence as you may have guess wrongly the y-intercept is not 2 since according to the definition the y-intercept is the y-coordinate when the x-coordinate is 0.
So how do you obtain the y coordinate.
You will first have to calculate the gradient of the line using the method described in this post.
The gradient in this case is 1.
You will use the equation y = mx + c and a coordinate on the line in this case (3,2).
y = 2
gradient = m =1
Hence the only variable left is c, the y-intercept.
3 = 1*2 + c
c = 3 – 2 =1
The y-intercept of the line is thus 1.
You should thus be very careful to check that the x-axis starts with 0 or does not start with 0 so as to choose which of the two methods to use.