Math 10 Week # 15

For week 15 of Math 10, we are once again continuing the trend and learning more about linear equations. This week however, we are getting into one of the most important things that we can learn about linear equations which is Slope.

Slope is a number that describes the steepness of a line. The slope is the same as the tangent ratio for a triangle and we can use slope to find out where to plot new coordinates on a graph. To explain the concept better, the Slope is the same as the equation rise which stands for the y axis or how much up of down the next coordinate in a linear equation will go and run standing for the x axis or how much to the right the coordinate will go. Before we move on, there are a few things that we need to include when talking about slope. Firstly, if the numerator or rise is positive, the line is increasing. Conversely, if the numerator or rise is negative, the line is decreasing. Next, the slope can only be calculated if you are comparing to coordinates both level on a line which means all numbers much be integers. Thirdly, if the numerator is larger than the denomiator, then it is a steep line and vise versa if the denominator is larger. So now that we got those out of the way, lets find out how exactly we can calculate the slope.

To start off, we are going to use a simple equation if used correctly. It is m = What this means is the y values between the two points will be subtracted from each other on the  top and the same but for the x values on the bottom. Once the subtraction is complete you divide the numerator by the denominator to determine the slope or if the number does not divide easily, the fraction is already the slope. Now we know how to do this, we will start with an example.

For our first example, we are going to find the slope between points (12, 2) and (8, 4). Like I wrote above, we are going to place the coordinates in place in the equation. So we are going to write our equation as m = Next, we are going to subtract the numbers from both the numerator and the denominator to end up with . Because we cannot evenly divide -5 by 12, we are going to keep the answer as it is being .

For our second example, we are going to calculate the slope between points (3, -6) and (8, 4). Like we’ve done previously, we are once again going to place the numbers into the equation. This equation starts with m = and we subtract the numbers in the fraction. Once this is done, we end up with . However, this time we have a fraction that can divide evenly so we divide -10 by -5 and once this is done, we end up with 2 as our final answer.