The slope characterizes the inclination angle to the horizontal axis (angular coefficient is numerically equal to the tangent of the angle). The slope is present in the equation of a straight line and is used in the mathematical analysis of the curves, where the slope is always equal to the derivative of the function. To better understand the slope, imagine that it affects the speed of function changing, that is, the greater the value of the slope, the greater the value of the function (with the same value of the independent variable).
The coefficient k in the line formula y = kx + b on the coordinate plane is numerically equal to the tangent of the angle, which constitutes the smallest turn of the Ox axis to the Oy axis, between the positive direction of the x-axis and a straight line.
The tangent of the angle can be calculated as the ratio of the opposite leg to an adjacent leg.
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