Blog Post #4

Hello Class! My name is Professor Bazerman and today I will be teach you how to find the slope of a function. What does this mean, you ask? Don’t worry, I will explain it step by step, comparing it to a real life example to paint a clearer picture in your head.


What is the slope?

• To put these terms into perspective, the slope of a function (or graph) refers to the steepness of the line. In other words, the slope can represent how steep the area is you want to build starts on. A horizontal line is completely flat, reaching from right to left. A vertical line is flat as well but reaches up and down. When we add the slope to the equation, we are able to determine how steep the line actually is. 

• Take the equation y=mx+b to represent the slope function. M represents the slope of the formula, meaning how far you will rise, over how far you will run.

• In regards to stairs, it is the size of one stair, going up (height/ rise), and then going across (width, run).
  
• Back to the equation... to find the slope, you must choose two points on the graph, each with an X & Y value.
  

• (2, 1)    (6, 3)
  (x1,y1) (x2, y2)

• Now, you must solve for M= SLOPE= Rise/Run--> m=y2-y1/ x2-x1

• Subtract the Y & X values, and then divide the Y value by the X value.
  m= 3-1/ 6-2
  m = 2/4
  m = 1/2

• plug in the value "m" into the equation
  y=1/2x+b

What does this mean?

• The graph moves vertically 1 and horizontally 2 to reach the next point on the graph or in our example to reach the next stair. 

Hope this helps! Stay tuned for our next lesson!