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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.
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
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
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