To add to martian's great reply, you can also represent a straight line using vector form:

p = (a) + t(b)

where a is a point on the line, and b is a vector along the line, and t is the parametric variable. Expanding the vector math gives

(x,y) = (c,d) + t·(u,v)

so

x = c + tu
y = d + tv

which is the parametric equation of a line. The parametric form is more useful when using vector math in 2D and 3D applications.


You can also represent a line that crosses the x-axis at (a,0) and y-axis at (0,b):

x/a + y/b = 1
or
xb + ya = ab (this allows a or b to be 0)
(Note this last one is really "ay + bx + c = 0" where c = -ab)

which is really just rearranging the numbers a bit. Here, a and b are the axis-intercepts, which may be more useful than knowing the slope and y-intercept in your standard y = mx + c equation.