Week 14 of Math 10 and Week 3 of quarantined classes. We haven’t shifted much from the properties of graphing, but we did learn a new topic which is Slope. In this blog post I will be explaining what slope is and how to solve for it.

Slope is a value that shows how steep or shallow a line is on a graph. This is the also the same as the tangent ratio because tangent’s opposite and adjacent sides can be substituted for the X and Y values on a graph. It’s commonly represented through , so if our line were to look like this

Then we just have to count how much the x value rises and how much the y value runs left or right. This is also known as the method. In this case right here our coordinates are (0,6) and (-3,0) so we start from the lowest point, go up or rise until we reach the second point, then run to whichever direction the second point is. The end result is or 2.

Another method to finding the slope is by finding all the “nice points” or the points of whole numbers where the line intersects, then find the within those points.

This is useful if you’re not given two specific points or if you want to try your hand at finding the slope faster than the first method. There are four different kinds of lines and slopes that you should also be aware of: Positive, Negative, Zero and Undefined.

The first two (Black and Green) are self-explanatory, they’re your typical sloped lines that face left or ride according to their x-value being negative or positive. The other two are a bit more complicated. Zero-sloped lines (Blue) are lines that have their y-value at 0, meaning there is no slope. Undefined lines (Red) are named as such because the x-value is zero, so the slope is essentially meaning that you’re trying to divide by zero (which isn’t possible, hence the undefined).

Next, I’m going to demonstrate how to find the slope using slope formula. Slope formula is and is used if given two coordinates. So if we were asked to find the slope between (6,4) and (3,2) it would look like this

Always remember to start with the y-values as the numerator, highlight it if you can. I’ve personally gotten a lot of questions wrong because I instinctively read the first number of the coordinate -or x- and put it on top which gave me the wrong answer. Another type of question you can encounter is if you’re given two coordinates with a missing value, like here

Here, it isn’t very different from the first method. Follow the slope formula then try to isolate the variable as if it was a person with COVID-19 who left quarantine. If you follow the order of operations you’ll likely get the right answer, just remember if you’re going to do something to one side, also do it to the other.

And that’s Slope!

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