Horizontal, vertical and diagonal straight line graphs
Categories: gcse graphs
In this section, we will look at some simple straight-line graphs and their equations.
Here is a video on this topic:
Horizontal lines
This graph shows a horizontal straight line:
We have marked a few example points that are on the line:
- (-2, 3)
- (1, 3)
- (3, 3)
Each of these points has the same y value of 3, and if you look at the line it is clear that any point on the line will have a y value of 3. So the line has the equation:
The formula of a graph defines all the points that are on the line. In this case, any points that have y equal to 3 are on the line and all other points are not on the line.
This line goes through 3 on the y-axis.
A line that goes through a on the y-axis has the equation:
The position of the line depends on the value of a:
- When a is greater than 0, the horizontal line is above the x-axis.
- When a is 0, the horizontal line is on the x-axis.
- When a is less than 0, the horizontal line is below the x-axis.
For example:
Vertical lines
This graph shows a vertical straight line:
These are points marked on the line:
- (2, -3)
- (2, 1)
- (2, 3)
Each of these points has the same x value of 2, and any point on the line will have an x value of 2. The line has the equation:
This line goes through 2 on the x-axis. A line that goes through a on the x-axis has the equation:
The position of the line depends on the value of a:
- When a is greater than 0, the vertical line is to the right of the y-axis.
- When a is 0, the vertical line is on the y-axis.
- When a is less than 0, the vertical line is to the left of the x-axis.
For example:
Remember that y = a defines all the points with the same y value, so is a horizontal line. x = a defines all the points with the same x value, so is a vertical line.
Main diagonal lines
Here is the main positive-going diagonal line:
This line goes through the origin, in an upwards direction. Here are some of the points the line goes through:
- (-3, -3)
- (1, 1)
- (2, 2)
Every point the line goes through has a y value that is equal to the x value, so the equation is:
Here is the main negative-going diagonal line:
This line also goes through the origin, this time in a downward direction. Here are some of the points the line goes through:
- (-2, 2)
- (2, -2)
- (3, -3)
In this graph, every point has a y value that is equal to the negative of the x value, so the equation is:
See also
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