How to Find the Slope of a Line
So, I’m assuming that you already know how to find the slope of a line when given the equation of a line.
We know that the standard form for the equation of a line is y=mx + b, where m is our slope and b is our y intercept.
We also know that slope is rise over run.
But now, how do we find the slope of a line when only given two points on a graph.
Let’s take a look. So, we have our graph.
So, we have two points on our line (1,3) and (3,7), but how do we find the slope of the line?
Well, we can do this by dividing the difference of the y coordinates of the two points you’ve been given by the difference of the x- coordinates from the same set of points.
Let me just write out, mathematically, everything that I just said.
So, we find the slope by dividing by the difference between our y coordinates. That can be written like this: Ysub2 – Ysub1 all over (because we are dividing) the difference between the x-coordinates. So, that is Y2-y1/x2-x1.
Now, you just need to plug in your y values and your x values.
But here is another very important thing, that many students get confused about… And it’s a great question: Which set of coordinates are my x1 and y1, and which set of coordinates are my x2 and y2.
The answer is: It doesn’t matter.
However, what you can’t do is assign x1 to the x value in a set of coordinates, and y2 to the corresponding y values. For example, in our points here on the graph, I couldn’t say that my 1 here (Point) will be my x1 and my 3 here (point) will be my y2. If I make my 1 here (point) x1 then my corresponding y coordinate has to be y1. What doesn’t matter is whether I make this (point) set of coordinates x1,y1, or this (point at other) set of coordinates x1,y1.
So now, let’s pick whichever point we want to be our x1,y1 and for this video I’ll just say that (1,3) will be our x1,y1, which makes (3,7) our x2,y2.
Now, lets plug in our values:
Since 7 is our y2, we have 7 minus our y1, which is 3. So, 7-3. Over x2, which is 3. Minus x1, which is 1.
7 minus 3 is equal to 4, and 3 minus 1 is equal to 2. So, we have 4/ 2, which reduces to 2 over 1.. Which is the same thing as 2.
Just to show you guys that it doesn’t matter which set of points you make your x1, y1, and x2,y2. I’ll switch them around.
So let’s make (1,3) x2,y2 and (3,7) x1,y1.
When, we plug them in we get 3-7 over 1-3. 3 – 7 equals -4, and 1-3 equals -2. When you have a negative divided by a negative you get a positive, giving you positive 4/2.. Which reduces to 2.
So, we see that our two answers are the same, and that it does not matter which set of coordinates we assign to be our x1,y1, and x2,y2.
I hope this video has been helpful to you.
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