Hello all, 
I am Professor Nina and I will be teaching you a lesson on "slope", today. 

Part A: 
What is slope? 
Every straight line can be represented by the term Linear Equation and by the equation y=mx+b, so a person can find coordinates of every point on the line, which will solve the equation if you substitute them in the equation for x and y. 

Slope Formula: The slope m of this line - its steepness, or slant - can be calculated like this:
                                            m = change in y-value
                                                   change in x-value
                                                   change in x-value




Also, in the linear equation for a line y=mx+b, m is the slope and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

As an example: A = (1,1) and B = (2,3) so if you plugged it in --> 
2 is the slope. This is a positive slope meaning that when you draw it on the graph it will rise from left to right.

An example for a negative slope  would be (0, -1) and (2, -5). Using the formula you would end up with the answer of -2, and when plugged in the line falls from left to right. 

Real life examples for slope include: road building. In the procedure of road building, there are two ways that slope can be used: slope to measure how steep the road is, which can either be portrayed as a percentage or decimal. The second way has to do with the middle of the road called the "crown", which is higher than the shoulder. The reason I mention this "crown", is because builders usually have a specific measurement on how large this slope must be in order to let water run off from the road into the gutter. 

Additionally, another example for slope is,  you have some steps in front of your building and you need to install a wheelchair ramp. The height above level ground of the stairs is 1.5 meters. The maximum slope that someone in a wheelchair can comfortably climb is 1:12 (1/12). You can use graphing and slope to determine how long your wheelchair ramp has to be in order to be within the building code.

I hope you enjoyed this lesson and now understand the full usage of slope.