The slope formula which is explained on this page, is used in calculus to find the gradient of a function in a given point or on a given interval.
This page contains an explanation about it and provides some exercises in order to get familiar with the formula.
The slope of a line is equal to the change in vertical direction divided by the change in horizontal direction. This is called rise over run.
If the interval is made very small, one can calculate the slope in a point.
The formula for calculating slope is as follows:
- A straight line starts at the origin of a coordinate system. What is the slope if it passes (3,7)?
- Point C(-5,8) is connected to point D(12,-12) with a straigth line. Calculate the slope.
- The maximum permissible slope for some road is 0.25. The change in height is 23 meters. What should be the minimal horizontal length?
- The function y(x) = x2 passes the point Z(4,16). Although this is a parabolic function instead of a straight line, the slope in point Z can be calculated by maken the interval very small. Try this.
- Δy/Δx = 7/3
- Δy/Δx = (12--5)/(-12-8) = -17/20
0.25 = 23/Δx
Δx = 92 meters
y(3.99) = 15.9201
y(4.01) = 16.0801
Δy = 0.16
Δx = 0.02
Slope = 0.16/0.02 = 8