# Horizontal, vertical and diagonal straight line graphs

In this section, we will look at some simple straight line graphs and their equations.

## 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:

$$ y = 3 $$

This line goes through 3 on the y-axis.

A line that goes through *a* on the y-axis has the equation:

$$ y = a $$

## 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:

$$ x = 2 $$

This line goes through 2 on the x-axis. A line that goes through *a* on the x-axis has the equation:

$$ x = a $$

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:

$$ y = x $$

Here is the main negative-going diagonal line:

This line also goes through the origin, this time in a downwards 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:

$$ y = -x $$

## See also

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