How to find the slope given two sets of points

Añadido: 2026-06-02

[00:00:09]Hello everyone, this is Mr. Souza and today we're going to learn how to find a slope given two sets of points.

[00:00:18]Your first step here is to write down the formula for slope.

[00:00:23]Which is Y2 minus Y1 over X2 minus X1.

[00:00:39]Your next step is to label your points.

[00:00:42]So, the points will always be given to you on this format here.

[00:00:47]X1 comma Y1 X2 comma Y2.

[00:00:59]Once you have that notice X1 is your first number, which is going to be four.

[00:01:08]Your Y1 corresponds to your second number, which is three.

[00:01:13]X2 is the first number of the second set, which is 12.

[00:01:19]And finally, Y2 is your last number, which corresponds to five.

[00:01:27]Once you have that, we have to go back to the formula, which states that the top, which is the numerator, it's Y2 minus Y1.

[00:01:37]So, Y2 in this case is five.

[00:01:43]minus your Y1 which again is your second number. So, in this case it's going to be three.

[00:01:53]over X2 So, again just look at your labels. X2 corresponds to 12.

[00:02:04]minus X1, which is your first number.

[00:02:08]So, it corresponds to four.

[00:02:14]Once you have that, you can go ahead and calculate.

[00:02:18]5 minus 3 will give you two.

[00:02:22]12 minus 4 is 8.

[00:02:27]But then, you may think you're done, but you're not done yet.

[00:02:31]You have to simplify.

[00:02:35]So, two and eight, they're both divisible by two.

[00:02:39]Therefore, we're going to divide the top and bottom by two.

[00:02:48]So, you have to simplify both numerator and denominator.

[00:02:52]Whatever you do to the top, you got to do it to the bottom.

[00:02:55]So, two divided by two in this case going to give you one.

[00:03:02]And 8 divided by two is going to give you four.

[00:03:06]Now, your slope is fully simplified, which is 1/4.

[00:03:10]Or, you may also write it as a decimal.

[00:03:13]So, if you put 1/4 in your calculator, that's going to give you 0.25.

[00:03:25]Okay?

[00:03:26]So, please go ahead, pause the video, and try question number two.

[00:03:43]Welcome back. Now, we're going to go over number two.

[00:03:47]Number two is not much different. Uh we're doing the same steps.

[00:03:52]So, you can start off by labeling your points x1 y1 x2 y2.

[00:04:01]I like to always label my points. That makes it easier to identify what's your x1, y1, x2, and y2.

[00:04:11]So, y2 goes first.

[00:04:14]In this case, that's going to be 10.

[00:04:19]Minus your y1, which is 7.

[00:04:25]Over x2, in this case is 12.

[00:04:31]Minus your x1, which is 8.

[00:04:37]10 minus 7 is going to give you 3.

[00:04:41]12 minus 8 will give you 4.

[00:04:45]And then we have to ask ourselves if we can simplify. In this case 3 and 4, the only common factor they have is 1.

[00:04:54]So, you're going to leave it like that.

[00:04:56]3 over 4.

[00:05:00]We can write as a decimal 0.

[00:05:05]75.

[00:05:10]Go ahead, pause the video and try question number three.

[00:05:26]Now, let's try question three.

[00:05:29]So, question three is going to be slightly different because of your negatives here.

[00:05:35]So, again, start the process by labeling your points x1 y1 x2 and y2.

[00:05:47]So, Y2 is 9 minus your Y1, which is a -3.

[00:05:56]So, we're going to place the -3 in parentheses cuz you're subtracting a negative.

[00:06:04]over -8 minus a -2.

[00:06:13]So, with that said, here's what's going to happen. Let's change the colors. We're going to have blue now.

[00:06:21]So, whenever you subtract a negative, you're going to switch that to a plus.

[00:06:30]Same thing here. Subtract a negative, we can switch that to plus.

[00:06:40]So, equals 9 and then instead of subtracting a -3, we're going to write 9 plus 3.

[00:06:51]Same thing with the bottom.

[00:06:54]-8 plus 2.

[00:07:02]9 plus 3 makes 12.

[00:07:07]-8 plus 2 makes -6.

[00:07:13]We're not done here because we have to simplify.

[00:07:17]12 happens to be divisible by 6, which is 2.

[00:07:22]However, we have a negative for the denominator, so you're going to write it as a negative 2.

[00:07:34]Okay.

[00:07:35]Please pause the video and try question number four.

[00:07:49]>> Welcome back. Now we're going to go over question number four.

[00:07:54]Again, your first step is to label your points, X1 Y1 X2 and Y2.

[00:08:06]Make sure you have that on your paper.

[00:08:08]So again, we use the formula Y2 - Y1.

[00:08:12]Your Y2 is going to be four.

[00:08:17]Minus your Y1, which is a negative one.

[00:08:21]So again, you're subtracting a negative.

[00:08:26]Over X2, which is going to be six.

[00:08:31]Minus X1 which is a negative four.

[00:08:40]So again, let me go ahead and change the color.

[00:08:48]Friendly reminder, when you subtract a negative it will become plus.

[00:08:55]Make sure you do the same on your paper.

[00:09:03]So here, you're going to have four plus one and six plus four.

[00:09:16]Four plus one will give you five.

[00:09:19]Six plus four will give you 10.

[00:09:24]Now, you may ask yourself, are we done yet? And the answer is no.

[00:09:29]Because five and 10 can be simplified by five.

[00:09:35]They're both divisible by five.

[00:09:37]So you're going to divide the top by five and the bottom by five.

[00:09:46]And once you do that, you're going to get one over two.

[00:09:53]Oops. There you go.

[00:10:00]So, one over two.

[00:10:02]Or again, you can write it as a decimal.

[00:10:05]>> [snorts] >> If you do one over two in the calculator, that's going to give you 0.5.

[00:10:15]Now, we're going to the last part of the lesson, which is common math misconceptions.

[00:10:32]Now, let's talk about common math misconceptions.

[00:10:36]A very common mistake students do is when they have zero over three, for instance, and they leave the solution like that.

[00:10:46]If you have zero over three, you must leave the solution as zero.

[00:10:54]Otherwise, it's not fully simplified.

[00:10:56]Therefore, it will not be correct.

[00:10:59]Now, another mistake is, let's say, if you have a four over zero.

[00:11:07]Students are inclined to say the solution is zero, and it's not zero. We cannot divide by zero. So, whenever that happens, your slope is undefined.

[00:11:23]Here's one way you can always remind yourself. If you get your calculator right now and try to divide four by zero, it's not going to work.

[00:11:46]>> [music]