Comparing different methods to find slope:
At the beginning of this week we learned how to find the slope of 2 points without a graph. Before, we were taught to count the rise and run from the boxes on a grid but without the grid lines it makes it pretty challenging to determine the slope of a line. This is where we would use a formula, this does the same thing it is just a different way to find slope. The only requirement is that we are given 2 coordinates with 1 x and y value each.
In an example below I will use the same two coordinates on a graph and in a formula to prove that you will still end up with the same slope no matter what method you use.
*the formula is y(#1) – y(#2) / x(#1 – x(#2) /// the first y in coordinate 1 subtract the y in coordinate 2 divided by the first x in coordinate 1 subtract the x in the second coordinate*
What you need to know:
- the first number in a coordinate is x
- the second number in a coordinate is y
- the second coordinate is 2
- the first coordinate is 1
- two negatives equals a positive (1-(-2) = 1+2)
- always y/x (remember this by rise=y & run=x // (rise/run)
Example:
Comparing slope:
We also learned about the term “collinear” this is a word used a lot in this unit of slope so it is important to understand its meaning. This term is referring to the relationship between 2 or more points/coordinates on a graph. In other words you are looking a weather the points all have the same slope. This also requires the use of the slope formula when you aren’t given a graph. The example below is demonstrating how to solve a question that is asking if points are collinear, with and without a graph (use of formula).
Collinear: is the slope of 3 or more points the same (do they line up to make a straight line)
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