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:
- Positive Slope
- Negative Slope
- Zero Slope
- Infinite Slope
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 roughly say that we will get an infinitely large number.
Why roughly? 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
The objective of this lesson is to show you under what circumstances, that the slope of a line is positive or negative.
Also, you will get to see in what way the slope becomes zero or infinite.
Now, consider this line. Since this line is parallel to the x-axis, the 'change in y' is 0.
Now, 0 divides by 4 gives 0.
Therefore, this line has the slope of zero.
Alright, As I move this point up, notice that the line slants upwards to the right, and the value of the slope increases.
Also, notice that the value of the slope is a positive number.
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.
Now, as the slope gets higher, this line will eventually becomes parallel to the y-axis.
Here, we can see something interesting, the slope is now infinite.
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.
Let's continue, as I move the point to the left, the line slants downwards to the right.
Notice that, we now have negative slope.
This is because of the 'change in x' is a negative number.
So, a positive number, divides by a negative number, gives a negative number.
As I move this point down, the slope gradually becomes zero.
Now, when I continue to move this point down, the line again slants upwards to the right again.
Notice that, the slope becomes positive.
As I move this point to the right, the value of the slope becomes higher.
Eventually, when the line is parallel to the y axis, the slope becomes infinite.
Let's continue to move further to the right, the slope now slants downwards to the right.
Notice that, the slope becomes negative.
Now, from these observations. we see that the value of the slope can be negative, positive, zero or infinite.
Let's examine positive and negative slope further.
It seems that when the line is slant upwards to the right, the slope is positive.
Further example, this line slants upward to the right and the slope is positive.
It is the same here, this line slants upward to the right and the slope is positive.
Finally, this line slants upward to the right and the slope is positive.
However, when the line slants downwards to the right, the slope is negative.
Further example, this line slants downward to the right and the slope is negative.
It is the same here, this line slants downward to the right and the slope is also negative.
Let's summarize on what we have observed, when we see the line slants upwards to the right, the slope is positive.
When the line slants downwards to the right, the slope is negative.
To briefly note, when the line is parallel to the x-axis, the slope is 0.
When the line is parallel to the y-axis, the slope is infinite.
That is all for this lesson, try out the practice question to further your understanding.
End of Transcript for Positive and Negative Slope
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