Transcript for Positive and Negative Slope

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The objective of this lesson is to show you under what circumstances, that the slope of a line is positive or negative.

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Also, you will get to see in what way the slope becomes zero or infinite.

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Now, consider this line. Since this line is parallel to the x-axis, the 'change in y' is 0.

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Now, 0 divides by 4 gives 0.

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Therefore, this line has the slope of zero.

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Alright, As I move this point up, notice that the line slants upwards to the right, and the value of the slope increases.

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Also, notice that the value of the slope is a positive number.

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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.

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Now, as the slope gets higher, this line will eventually becomes parallel to the y-axis.

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Here, we can see something interesting, the slope is now infinite.

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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.

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Let's continue, as I move the point to the left, the line slants downwards to the right.

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Notice that, we now have negative slope.

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This is because of the 'change in x' is a negative number.

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So, a positive number, divides by a negative number, gives a negative number.

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As I move this point down, the slope gradually becomes zero.

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Now, when I continue to move this point down, the line again slants upwards to the right again.

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Notice that, the slope becomes positive.

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As I move this point to the right, the value of the slope becomes higher.

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Eventually, when the line is parallel to the y axis, the slope becomes infinite.

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Let's continue to move further to the right, the slope now slants downwards to the right.

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Notice that, the slope becomes negative.

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Now, from these observations. we see that the value of the slope can be negative, positive, zero or infinite.

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Let's examine positive and negative slope further.

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It seems that when the line is slant upwards to the right, the slope is positive.

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Further example, this line slants upward to the right and the slope is positive.

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It is the same here, this line slants upward to the right and the slope is positive.

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Finally, this line slants upward to the right and the slope is positive.

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However, when the line slants downwards to the right, the slope is negative.

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Further example, this line slants downward to the right and the slope is negative.

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It is the same here, this line slants downward to the right and the slope is also negative.

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Let's summarize on what we have observed, when we see the line slants upwards to the right, the slope is positive.

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When the line slants downwards to the right, the slope is negative.

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To briefly note, when the line is parallel to the x-axis, the slope is 0.

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When the line is parallel to the y-axis, the slope is infinite.

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That is all for this lesson, try out the practice question to further your understanding.

End of Transcript for Positive and Negative Slope