Positive & Negative Slope
This lesson shows you under what circumstances a line can have a negative slope, positive slope, zero or infinite slope.
About This Lesson
After you have familiarized with the slope formula. It is time to further analyze the slope of a line.
In this lesson, we will see under what circumstances a line can have:
You should proceed by reading the
and watch the
below. After that, you can try out the
Understand how the 'change in y' and 'change in x' are calculated. To recall them, you can watch the first math video in the
slope of a line lesson
It is useful to learn about the
so that it will be easier to understand this lesson.
We will come across something called 'infinite slope'. To comprehend it, let me explain 'infinitely large number' first in a simple way.
Observe the following sequence:
2 ÷ 0.1 = 20
2 ÷ 0.001 = 2000
2 ÷ 0.00001 = 200000
2 ÷ 0.0000001 = 20000000
2 ÷ 0.000000001 = 2000000000
2 ÷ 0.00000000001 = 200000000000
2 ÷ 0 = infinitely large number
Notice that when 2 is divided by a smaller number, you will get a larger number. Now, if 2 is divided by 0, we can
say that we will get an infinitely large number.
? This is because it would be more accurate to say that the number is 'undefined'. But, for the sake of simplicity, I will not explain this for now.
Now, watch the following math video to learn more.
Click play to watch video
Math Video Transcript
Transcript for Positive and Negative Slope 00:00:01.240 The objective of this lesson is to show you under what circumstances, that the slope of a line is positive or negative. 00:00:09.010 Also, you will get to see in what way the slope becomes zero or infinite. 00:00:14.080 Now, consider this line. Since this line is parallel to the x-axis, the 'change in y' is 0. 00:00:23.100 Now, 0 divides by 4 gives 0. 00:00:27.110 Therefore, this line has the slope of zero. 00:00:30.220 Alright, As I move this point up, notice that the line slants upwards to the right, and the value of the slope increases. 00:00:39.090 Also, notice that the value of the slope is a positive number. 00:00:44.010 This is because the 'change in y' and 'change in x' are positive. Hence, a positive number divides by a positive number gives a positive. 00:00:54.210 Now, as the slope gets higher, this line will eventually becomes parallel to the y-axis. 00:01:01.110 Here, we can see something interesting, the slope is now infinite. 00:01:06.160 This is because of the 'change in x' is zero, and for the case of slope, any non zero number divides by 0 gives infinite. 00:01:15.160 Let's continue, as I move the point to the left, the line slants downwards to the right. 00:01:21.180 Notice that, we now have negative slope. 00:01:25.100 This is because of the 'change in x' is a negative number. 00:01:29.220 So, a positive number, divides by a negative number, gives a negative number. 00:01:36.220 As I move this point down, the slope gradually becomes zero. 00:01:42.180 Now, when I continue to move this point down, the line again slants upwards to the right again. 00:01:50.030 Notice that, the slope becomes positive. 00:01:54.140 As I move this point to the right, the value of the slope becomes higher. 00:01:59.140 Eventually, when the line is parallel to the y axis, the slope becomes infinite. 00:02:06.030 Let's continue to move further to the right, the slope now slants downwards to the right. 00:02:12.090 Notice that, the slope becomes negative. 00:02:16.040 Now, from these observations. we see that the value of the slope can be negative, positive, zero or infinite. 00:02:24.050 Let's examine positive and negative slope further. 00:02:29.050 It seems that when the line is slant upwards to the right, the slope is positive. 00:02:35.140 Further example, this line slants upward to the right and the slope is positive. 00:02:42.130 It is the same here, this line slants upward to the right and the slope is positive. 00:02:48.030 Finally, this line slants upward to the right and the slope is positive. 00:02:54.060 However, when the line slants downwards to the right, the slope is negative. 00:03:00.180 Further example, this line slants downward to the right and the slope is negative. 00:03:06.210 It is the same here, this line slants downward to the right and the slope is also negative. 00:03:15.030 Let's summarize on what we have observed, when we see the line slants upwards to the right, the slope is positive. 00:03:23.180 When the line slants downwards to the right, the slope is negative. 00:03:29.130 To briefly note, when the line is parallel to the x-axis, the slope is 0. 00:03:37.010 When the line is parallel to the y-axis, the slope is infinite. 00:03:43.070 That is all for this lesson, try out the practice question to further your understanding. End of Transcript for Positive and Negative Slope
Practice Questions & More
Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.
You can start by going through the series of
questions on positive and negative slope
or pick your choice of question below.
on positive and negative slope.
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