in this video we're going to cover how to do questions like this one where we need to find the gradient between two points but we're not given the graph that they're from the normal way you'd find the gradient is using this equation here where we divide the change in y by the change in x however if we're only given coordinates rather than the graph then it's easier to use this equation which is basically the same thing but tells us that we can find the change in y by doing y2 minus y1 because that will just give us the difference between the y values and we can find the change in x by doing x 2 minus x 1. the tricky thing with this equation though is knowing what all of these x and y's mean but actually they just represent the x and y values of our two coordinates so x1 and y1 are the x and y values of the first coordinate meaning x1 is 2 and y1 is 3 whilst x2 and y2 are the x and y values of the second coordinate so x2 is 8 and y2 is 12. it doesn't actually matter which set of coordinates you choose to put as the first and the second but in general it'll be easier to work out if you put the biggest numbers as the second set so because 8 and 12 are bigger numbers than 2 and 3 we put 8 and 12 as x2 and y2 so now that we have our formula and we know what all the x and y's are we just plug the values into the formula so for y2 minus y1 we'll have 12 minus 3 on the top and for x2 minus x1 we'll have 8 minus 2 on the bottom then we can simplify this to get 9 divided by 6 and that would just be 1.5 so we know that the gradient between our two points is 1.5 to give this some more practice let's have a look at this one where we need to find the gradient between the points 11 7 and 8 negative 2. so the first thing we need to do here is choose which pair is going to be the first coordinate and which is going to be the second and remember it's normally easiest if we make the bigger coordinate the second one so we'll make 11 7 a second meaning that 11 is x2 and 7 is y2 so 8 is x1 and negative 2 is y1 then all we have to do is plug these numbers into our formula so on the top we'll have 7 minus negative 2 and for the bottom we'll have eleven minus eight which simplifies to nine over three which is just three so the gradient between our two points is three one last thing that i want to point out is that we can also use this method even if we are given a graph because we can just pick two points on the line and then use those coordinates so for this question where we need to calculate the gradient of the line we'd start by picking any two points along the line like these two and then label them both so 0 negative 1 and four negative seven next we need to choose which ones can be the first coordinate and which one is going to be the second but it doesn't really matter this time because this one has the bigger x value but this one has the bigger y value so we'll just pick this one to be our first and this one to be our second and now that we know what all the values are we just plug them into our formula so negative seven minus negative one over four minus zero giving you negative six on top and four on the bottom so you just do negative six divided by four which is negative 1.5 and that's your answer anyway that's everything for this video so i hope that was helpful to you if it was then please do give us a like and subscribe and cheers for watching