With an altimeter and an odometer, we travel the exact route we measured on the map and our altimeter indicates a change in altitude of 396 feet which, not surprisingly, is precisely what we had already measured on the map. Grade = (rise ÷ run) * 100 grade = (396 ÷ 15,840) * 100 = 2.5%Ĭalculating Grade By Measuring The Road Distance One way to calculate the grade of a hill is with a map that shows the altitudes of locations.įor example, you've measured out a distance of 3 miles (run) with a change in altitude of 396 feet (rise).įirst, the units must be made consistent, so we convert 3 miles to 15,840 feet. Stating this as an angle of 2.8624 degrees doesn't give you much of an idea how the rise compares to the run. Stating this as a percentage, whatever horizontal distance you travel, your altitude increases by 5% of that distance. Stating a ratio such as 1 in 20 tells you immediately that for every 20 horizontal units traveled, your altitude increases 1 unit. Of these 3 ways, slope is expressed as a ratio or a grade much more often than an actual angle and here's the reason why. Slope, tilt or inclination can be expressed in three ways:ġ) As a ratio of the rise to the run (for example 1 in 20)Ģ) As an angle (almost always in degrees)ģ) As a percentage called the " grade" which is the (rise ÷ run) * 100. Just enter you own examples above and they will be calculated immediately step-by-step.Bicyclists, motorists, carpenters, roofers and others either need to calculate slope or at least must have some understanding of it. To find the equation of the function, you have to insert a point and get an equation which gives the y-axis intercept. To calculate the slope m, use the formulaĪs we can see, the slope was calculated first. This means: You calculate the difference of the y-coordinates and divide it by the difference of the x-coordinates.
#Slope of a graph m generator how to
How to calculate the equation of a linear function from two given points?įirst, we have to calculate the slope m by inserting the x- and y- coordinates of the points into the formula.
Therefore, the equation of the function is General form of the linear function: f(x)=mx+b Here is an example: Lets assume we know that our function has slope and goes through (-2|5).Ĭalculate the y-axis intercept b by inserting: the one coordinate for x and the other one for f(x). You have to insert the point into the equation, i.e. How to calculate the equation of the line from a point and the slope? If you take a look on the function graphs, you see that intersects the y-axis at intersects the y-axis at. As the name says, it says where the function cuts the y-axis. The y-line intercept is the number at the end of the function. What is the y-line intercept of a linear function? This means whenever we go one square to the right, we have to go three squares down to be on the graph again. If we go one square to the right of any point on the graph, we have to go two squares up to be on the graph again.Īnother example, this time with negative slope: It says how may units you have to go up / down if you go one unit to the right.
The slope of a linear function corresponds to the number in front of the x. The graph of a linear function is always a line.Ī similar word to linear function is linear correlation. Here is an example:ĭein Browser unterstützt den HTML-Canvas-Tag nicht. The general form of a linear function is, where m is the slope and b is the y-axis intercept. A linear function is a function whose graph is a line.