Slope, pitch, ratio, rate, gradient, obliqueness, rise over run, steepness, sway, or whatever you want to call it, it's all the same thing. In math we write equations in a particular form. A linear equation is one that does not have an exponent on the variables. The Slope-Intercept form of a linear equation is y = mx + b, or - if you prefer - f(x) = mx + b.

Lot's of professions use slope everyday. There's a slope calculator available at **www.blocklayer.com**.

Excellent question! let's take two points, say (1, 4) and (3, 5). Were you to plot these two points you would count over to the right on the horizontal x axis one space. And up 4 spaces on the vertical y axis.

You would do this because, on a Cartesian coordinate system (a fancy name for the x/y graph we're all pretty much used to - in the 1600's a french mathematician named Descartes liked to use Latin to name things, the actual word was Cartesius but - I digress).

So, the first point would be at (x, y) or (1, 4) or one to the right and 4 up. The second point would be plotted 3 to the right and 5 up. If the coordinates were negative we'd go to the left and then down. Draw a straight line through those two points, extend it to infinity in both directions, and that's all the possible values of x and y.

But, being the kind of guy who doesn't trust drawings, we can also find out a lot about the equation of the line by looking at those two points. In 2 dimensional space, we only need two points to define a line. So, we use the rise divided by the run to determine the slope. The common phrase for this is rise over run. The rise is formed by the second coordinate or y coordinate, since this is the axis we rise and fall on. It's vertical and goes up and down. The run is the first coordinate or x coordinate. We are interested in change. So, subtract the y's and divide that by the result of subtracting the x's.

(y - y)/(x - x)

Using the points (1, 4) and (3, 5) the slope would be (4 - 5) / (1 - 3) = (-1) / (-2) = 1/2.

As long as you keep the pairs in order, you get the same answer if you did (3, 5) and (1, 4)

(5 - 4) / (3 - 1) = 1/2

Super important formula. In this equation the y is a dependent variable (it's value depends on what value we assign to x). The m is the slope, we're multiplying it times x and that makes the line tilt. The x is the independent variable (we can make it whatever we want). And the b is the y intercept. Note that when x = 0 we get y = 0x + b or y = b. So, when x = 0 the line will intersect the y axis at b.