Week 12 – Math 10 – Slopes

This week in Math 10, I have chosen to talk about slopes.

The slope is the number that describes the steepness of a line. It is equal to the tangent ratio in trigonometry, and concepts from trigonometry frequently tie in to slopes. The slope can be described as $\frac{vertical distance}{horizontal distance}$ but more easily described as $\frac{rise}{run}$

The slope can be calculated using two points on the line which you want to calculate the slope of; as an example, I will use the plane coordinates (-1, 6) and (5, -1). As a reminder, those coordinates are ordered pairs, which are formatted as (x, y) with x representing horizontal coordinates and y representing vertical coordinates.

The first equation to calculate slope is $\frac{y_1 - y_2}{x_1 - x_2}=m$ but can also be calculated with the subscript order swapped; the subscripts being which coordinates are being used in what order, and M representing the slope.

$\frac{6-(-1)}{-1-5}=m$

We now simply evaluate the top and bottom of the fraction to get M.

$\frac{6-(-1)}{-1-5}=\frac{7}{-6}$

The other method of calculating slope is by calculating the tangent of the line if it were a right triangle; this is done by calculating the vertical and horizontal distances between the points, done by finding the difference between the x and y coordinates of each point respectively.

-1-5=6=run

6-(-1)=7=rise

We now know the horizontal distance is 6, and vertical distance is 7. Now, we calculate the tangent of this triangle using the lowest point as a reference, in order to maintain $\frac{rise}{run}$

$\frac{7}{-6}$

Cameron's Blog_

Now with an underscore, because there's 6 of us

Week 12 – Math 10 – Slopes

Leave a Reply Cancel reply