1. y=x/3

2. y=-3x-2

Two linear equations (i.e., their graphs are straight lines).

y = mx + b is the most common form you will see.

m is the slope or "rise over run".

b is the y-intercept or where the graph crosses the y-axis when x = 0.

[1] m = 1/3, b = 0

[2] m = -3, b = -2

The slope can be determined by use two points (x1, y1), (x2, y2):

(y2 - y1) / (x2 - x1)

Want more?

Think of the Pythaorean Theorem: c^2 = a^2 + b^2 where (c) is the length of a hypotenuse (the longest side) of a right triangle, and (a) and (b) are the lengths of the other two sides.

Form this information you can also derive the distance formula (point-to-point on a graph), the midpoint formula, and the slope of a line.

It is a good mnemonic device.

The slope is also the "tangent" to the angle opposite the right angle if you use the two points as two ends of the diagonal of a right triangle, and then draw the rest of a right triangle using that diagonal.

That may sound complicated, but a picture would make it very clear. By the time I downloaded a picture, you may have already drawn a right triangle for yourself.

One of these days this information about a right triangle will ease your understanding when you get into differential calculus.