Linear Graphs
(Straight Lines)

Vertical Lines:

$$x=k$$

where $k$ is some constant, e.g., $x=3$. This is the equation of a vertical straight line.

Horizonal Lines:

$$y=k$$

where $k$ is some constant, e.g., $y=-2$. This is the equation of a horizonal straight line

Lines at other Angles:

$$y=mx+c$$

where $m$ and $c$ are constants, i.e., $y=2x+4$

$m$ is the gradient of the line. Gradient,

$$m=\frac{\mathrm{change\; in\; y}}{\mathrm{change\; in\; x}}=\frac{\Delta y}{\Delta x}$$

$c$ is the y-axis intercept [$\frac{\mathrm{-c}}{m}$ is the x-axis intercept]

The line maybe written in either of these less usual forms:

$$x-k=0$$ $$y-k=0$$ $$ax+by+c=0$$ $$ax+by=c$$