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.

Question

AskIITians Expert Hari Shankar IITD · Answer

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

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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.

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.

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