By EasyHow
How to find the slope of the straight
The angular coefficient of the straight line — coefficient k in the equation y = kx + b of a straight line on the coordinate plane is numerically equal to the tangent of the angle (which is the smallest rotation from axis Ox to the axis Oy) between the positive direction of x-axis and the straight line.
Instruction
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.
Note
Since the coefficient is equal to the tangent of the angle of inclination, the angle varies from -90 degrees to +90 degrees.
Useful advice
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.
