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Vishrant Vasavada Grade: 11
        If a line crosses from Y-axis and X-axis at two points respectively in such a way that it makes Angle of 45 in clock-wise direction with X-axis, find dy/dx.
7 years ago

Answers : (1)

AskIITians Expert Hari Shankar IITD
17 Points
										

For any line, dy/dx is its slope.


If the line makes an angle of 45 degree wit the x-axis in clockwise direction,


it means that it makes an angle of -45 deg in anti-clockwise direction.


Slope = tan(angle made with x-axis)


Therefore,


Slope = tan(-45 degree) = -1


Hence,


For this line,


dy/dx = -1


 


Another method:


Slope or dy/dx is the rate at which y changes with respect to x.


Here, the angle which the line makes with x- axis is 45 degree.


Lets say we move one unit along the x-axis.


Since the angle with x-axis is 45 degree,


We move


(1)(tan45)  = (1)(1) = 1 unit alon the y-axis as well


But since the line is going downwards if we move along positive x-axis, we can see that the line will be moving one unit downward along y-axis.


Hence, change in y = -1


Change in x = 1


So, slope  =  -1/1  = 1


dy/dx = -1

7 years ago
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