How to find the slope
Under slope usually understand the slope of the tangent line of any function. However, you may also need the ability to find the slope of the normal line, for example, one of the sides of a triangle with respect to the other. After determining that you need to find, operate one of the following methods.
Instruction how to find the slope
If you need to calculate the angle of the line to the horizontal axis, and you do not know the equation of the line, drop from any point on this line (in addition to the axis intersection point) perpendicular to the axis. Then measure the legs of a right triangle obtained and find the ratio of the adjacent leg to an opposite. The resulting number will be equal to the slope. This method is useful not only for the direct study of inclination angle but also for measuring any angles as in the drawing, and in life (for example, the angle of slope of the roof).
If you know the equation of the line, and you need to find the slope of this line to the x-axis, express y in terms of x. As a result, you get an expression of type y = kx + b. Note the coefficient k - this is the tangent of the angle between the positive direction of the axis Ox and the line of a straight line should be positioned this axis. If k = 0, the tangent is also zero, that is, a direct parallel to or coincident with the x-axis.
If you are given a complex function such as quadratic, and you need to find the slope of the tangent to this function, or, in other words, the slope, calculate the derivative. Then calculate the value of the derivative at a given point, to which will be held tangent. The resulting number is the slope of the tangent. For example, you are given the function y = x ^ 2 + 3x, considering its derivative, you'll get an expression u` = 2x + 3. To find the slope at the point x = 3, substitute this value into the equation. As a result of simple calculations, you can easily get y = 2 * 3 + 3 = 9, this is the desired tan.
In order to find the slope of one side of the triangle to the other, proceed as follows. Find the sine (sin) of the angle and divide it by the cosine (cos), as a result you get the tangent of this angle.