![]() ![]() This worksheet does not have any answers however the answers can be checked using the Gradient Slope Calculator available at the following link:Ĭlick the following link to get to the worksheet.Ĭlick here for Gradient Slope Formula Worksheet It also tells us about Parallel and Perpendicular Lines.Ĭlick the following link to use this interactive calculator. Straight Line Between Two Points CalculatorĪll we have to do is enter the (x,y) coordinates of any two points and click “Go” and this online interactive will calculate the slope, find the rule for the line, and even plot the line for us on an X-Y Grid. The video even shows the calculation of zero and undefined gradients using the formula. The following is an excellent, but quite long YayMath video, which uses the Gradient Slope Formula. This next video talks about the change in y versus the change in x, using the Gradient Slope Formula. The following is a Gradient by Formula video, (10 minutes long), that shows the line plotted and how the formula works. Here is the fully worked solution to Example 2. it is so much faster to get to the answer! This is the great thing about using the Gradient Slope Formula…. ![]() In this example we have not bothered plotting the points, because this is not necessary. (It can be checked by counting squares on the Grid, and is Negative because from left to right it is a Downhill Line connecting the two points. Here is the fully worked solution to Example 1. (You can then scroll down to see the fully worked solution). Have a go at substituting the required values into the Gradient Formula, and working out the final answer. ![]() HOWEVER, Graphing the points is not actually necessary, as we shall see in Example 2 later. In this first example, we have plotted the points and graphed them on a Cartesian Grid. To get the Gradient we divide these two subtractions.Īpplying this formula to our previous example points, we obtain the same Gradient Slope answer of “2”. This gives us the “Change in Y” and the “Change in X”. The Gradient Slope Formula involves labelling the x and y coordinates, and then subtracting the y’s and subtracting the x’s. This observation led mathematicians to develop a Gradient Slope Formula which does the coordinate pairs subtractions. We can actually determine the UP and ACROSS squares counts by SUBTRACTING PAIRS OF X AND Y COORDINATES. Previously we have found Gradient Slope by drawing our points onto a grid and counting squares. The Mathematical value of a Gradient or Slope involves comparing how far up we have gone, against how far across. Image Copyright 2013 by Passy’s World of Mathematics The nice thing about the formula method, is that we do not actually need to draw the points onto a Cartesian Plane Grid. In our “Gradient Formula” lesson, we will be looking at finding the Gradient Slope between two points using an Algebra Formula. If you have not done this previous lesson, then you need to go through the material at the link below, before doing the “Gradient Formula” lesson. ![]() In a previous lesson we looked at Gradient and Slope, and how to calculate them by plotting points on a Grid, and drawing and measuring right traingles. Obviously some basic mathematical calculations would have been involved with building this jump ramp. The Gradient Slope of the Snowboard Jump Ramp in the photo above, would need to be created at the correct incline to give the Snowboarder sufficient height to complete his aerial acrobatics. ![]()
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