Calculating the Slope of a Line

Hello! My name is Savanna and today we are going to talk about how to calculate the slope of a line, and the different types of functions that we look at when making or analyzing graphs and finding the slope. When we think of linear equations we know that there are three main types of functions: slope intercept, point-slope, and standard.

What is a function? A function relates an input to an output- in a function there is one output for every single input.
Here are three main functions for the equation on a line (linear functions). Within these forms of functions there are different symbols that refer to slope.
To find a slope in the simplest way possible, we can use different methods according to the situation. However, sometimes we have to solve an equation to find the slope mathematically. Here are the linear equations we need to solve to find the slope of our given lines.

An important note: slope always= rise over run, or the height over the width. If you have two points on your graph (see point=slope form below) one can calculate the slop using these two points and rise over run. (y2-y1)/(x2-x1)

-Slope intercept is my personal favorite, and generally easy to remember.
Y=mx +b, where "m" is the slope and "b" is the y intercept. easy enough to decipher.

   Example:
   y=6x -5
   Here, we can clearly see that the slope is given to us as "m" in this case is 6. The slope is 6.

-Standard form is also easy to understand but a little less straight forward.
  ax +by=c, where both "a" and "b" cannot equal zero. In standard form, to find the slope we solve for   x and graph it.

   Example:
   2x + y= 4
   2x=4-y
   x=2-2y
   You find both the x and y intercepts by solving the equation and then through graphing, one can see    find the slope.

-Point-Slope form is less often used but still valid.
   y2-y1=m(x2-x1)
   Here, the slope is given again using the letter "m". We know the slope already, as in slope intercept,    which helps us to further graph the line.

After today we now know the three different types of linear equations and we can now go off and solve these formula in order to find the slope of the line. :) Class dismissed!