# Linear graphs

**Coordinate pairs**

Coordinates are written in pairs called the “coordinate pair” and in the following format (*x*, *y*). Here, the *x* represents the *x*-cordinate and the *y* represents the *y* coordinate.

**Graphs parallel to the ***y*-axis

*y*-axis

Where *x* = *c,* a graph will be parallel to the *y*-axis and will cut the *x*-axis as the point (*c, 0*). For example: where *x* = -10, *x* = -3, *x* = 4, *x* = 9 the following graph represents this line. In these scenarios, *y* can be any number.

Point to note: In this scenario, the lines will always be vertical and parallel to the *y* axis.

**Graphs parallel to the ***x*-axis

*x*-axis

Similar to* x* = *c*, where *y* = *c*, *c* can be any number which is parallel to the *x*-axis. For example, the graph below displays where *y* = 5, *y* = 3, *y* = -2 and *y* = -5

Point to note: the *y* = *c* graph will always be parallel to the *x*-axis and therefore be horizontal.

**Plotting graphs of linear functions**

When plotting the graphs of a linear function, the *x-*coordinate and the *y-*coordinate pair can be linked by a function. For example:

*y* = *x* – 2 can be represented using the following coordinate pairs:

(1, -1), (4, 2), (-2, -4), (0, -2)

To plot these coordinate pairs in a graph, a **table of values** will need to be constructed:

For the following function *y* = 2*x* + 5, the following table is used:

This is then used to plot its graph as shown below: