Slope of a line

Practice

Now , let's try some MCQ questions to understand this lesson better.
You can start by going through the series of the graphing linear equations questions below

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What is in this video ?

• 00:00:02.130
  This lesson will explains to you on how to calculate the 'change in x' and 'change in y'.
• 00:00:10.240
  When you do the calculation, it is important to first run, and then climb. What does this means?. The following example will explain it.
• 00:00:24.150
  Imagine, that you are at this point right over here with x-coordinate of 2. Now, you run towards the right, notice that your x-coordinate increases..
• 00:00:37.080
  Now, you see that your current x-coordinate is 5. You can calculate the change in x, by taking the current x-coordinate, 5, minus the original x-coordinate, 2. This gives the change of x of 3
• 00:00:56.110
  Now, let's take a look at the change in y. You are currently at this point with y-coordinate of 2. When, you climb up from here, your y-coordinate increases. (Increase y-coordinate from 2 to 5).
• 00:01:11.020
  You see that now, your y coordinate is 4. You can calculate the change in y, by taking the current y-coordinate, 4, minus the original y-coordinate, 2. This gives the change of y of 2.
• 00:01:28.170
  Alright, for this example, you have the 'change of x' equals to 3, and 'change of y' equals to 2 . Let's take a look at another example.
• 00:01:43.130
  Imagine, that you are at this point right over here with x-coordinate of 3. When you run towards the left, your x-coordinate decreases.
• 00:01:57.230
  Now, you see that your current x-coordinate is negative 2. You can calculate the change in x, by taking the current x-coordinate, negative 2, minus the original x-coordinate, 3. This gives the change of x of negative 5.
• 00:02:17.050
  Now, let's take a look in change in y. When you climb up from here, your y-coordinate increases. (Increase y-coordinate from -4 to 2).
• 00:02:31.010
  You see that your current y coordinate is 2. You can calculate the change in y, by taking the current y-coordinate, 2, minus the original y-coordinate, negative 4. This gives the change of y of 6.
• 00:02:48.240
  Alright, for this example, you have the 'change of x' equals to negative 5, and 'change of y' equals to 6 .
• 00:02:58.020
  With these two examples, you should be able to calculate the 'change in x' and 'change in y.' That is all for this lesson. The next lesson explains the slope of a line.

• 00:00:02.120
  After the lesson on graphing, it is time to learn about the slope of a line.
• 00:00:12.190
  If we were to put 2 points here, you will see that we can draw a line through these points.
• 00:00:19.200
  As obvious as it seems, notice that if i move the point up, the line changes.
• 00:00:26.170
  If you were to observe carefully, one of the things that changes here is the slope of the line. The slope of this line increases further when I move this point up.
• 00:00:38.070
  Now that you know this, the next question is can the slope be assigned a meaningful number? The answer is yes. But, how do we do it?
• 00:00:51.110
  With some thought, the most logical way to do this is to take the ratio of the 'change in y' and 'change in x'.
• 00:01:01.180
  As an example, let's imagine that, you run from this point from here to here. In this case,the change in x is 2. When you climb from here to the point above, the change in y will be equals to 3. So, the slope for this case is 3.0 divided by 2.0, which is 1.5.
• 00:01:29.030
  Getting a clearer picture of the slope now? Let's look at the 'change in x' and 'change in y' in more detail.
• 00:01:37.150
  Let me show you the x-coordinates of these points. When you run from here to here. The change in x is 4.0 minus 2.0 which equals to 2.0. Or, simply looking at the grid, 1, 2.
• 00:01:56.210
  For change in y, let me show you the y-coordinates first. When you climb from here to here, the 'change in y' in this case is 5.0 minus 2.0 which is equals to 3.0. Or, simply looking at the grid, 1 , 2 , 3.
• 00:02:20.100
  Let's explore further, see what happens when i move this point around.
• 00:02:25.180
  When i move it to the left, observe what happens.
• 00:02:37.090
  Now, when you run from here to here, the change in x is -4.0.
• 00:02:45.100
  When you climb from here to here, the change in y is 3.0.
• 00:02:51.200
  From this, the slope of this line is 3.0 divides by negative 4.0 which gives negative 0.75. Let me emphasize, the slope now is a negative number.
• 00:03:02.050
  That is all for this lesson. You can move on to the practice questions to test your understanding.

Now , let's try some MCQ questions to understand this lesson better.
You can start by going through the series of the graphing linear equation question below