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Write the equation of a straight line and Express the ordinate of a function through the x point. For example, let the equation of the line: 3x + 4y = 13. Express the y coordinate: y = -3x/4 + 13/4.
The coefficient in front of x will be the slope of a straight line in the Cartesian coordinate system. That is, the slope of k=-3/4.
To find the angle between line and x-axis, it is sufficient to calculate the arc tangent of the angular coefficient. Thus the angle between line 3x + 4y = 13 and x-axis is equal to: U = artg(-3/4) = -36 degrees.
Since the coefficient is equal to the tangent of the angle of inclination, the angle varies from -90 degrees to +90 degrees.
Knowing the coordinates of a direction vector of the straight, you can always find the angle between it and the x-axis, and hence the slope of the straight line.