 Hi, I'm Lucy and in this video, we're going to learn how to find the gradient of a straight line from a graph. The gradient tells us how steep a line is, like how steep a hill or a mountain is, and the steeper is the bigger the gradient. On graphs, though, we do need to be careful because lines going in this direction have a positive gradient, whereas lines going in this direction have a negative gradient. Straight line graphs are found everywhere, like for comparing fuel consumption, currency conversions, and for comparing data. Sometimes you are given a straight line and you need to find its gradient because the gradient tells us some important information. Like on a distance time graph, the gradient is the speed, or on a currency conversion curve, it tells us the exact conversion rate. So, looking at this graph, we straight away know that it is a positive gradient because it is in this direction. Right, so for finding the gradient, you take any two points on the line, but make sure they have to be exact coordinates. So these ones are good, zero negative three and four three. But these ones, for example, aren't so good. Two and a half and about zero point seven and five and a half and about five point two five. With your two points, draw a triangle and how much the triangle goes up, the rise, which is six, and how much the triangle goes along the run, which is four. All you need to remember is that the gradient is the rise over the run, or the change in Y divided by the change in X. So for our line, gradient is rise over run, so six divided by four, which we simplify, so the gradient is positive three over two. So give this one a go yourself. Follow the exact same process, so take two points, and the only difference is that the gradient is going to be negative because it's going in the negative direction. Pause the video, work out the answer, and click play when you're ready to check. Did you get a negative two? If you got it right and you want to skip the explanation, click here. Otherwise, keep watching. So I'm going to choose these two points, but you may have chosen different ones. The rise is six and the run is three. So gradient equals rise over run, so six divided by three, which we simplify, the gradient is negative two. Remembering it is negative because it is going in this direction. But what do these numbers really mean? A gradient of three over two and a gradient of negative two. Look at the graph. A three over two gradient means that for every two squares we go along, we go up three. And then a negative two over one gradient, every time we go along one, we go down two. So there you have finding the gradient of a straight line from the graph. You just need to remember to take two points on the line, and then using gradient as the rise over the run, or the change in y over the change in x, you can easily find the gradient. But be careful because lines going in this direction have a positive gradient, but lines going in this direction have a negative gradient. In the next video, we're not just going to look at finding the gradient, we're going to find the equation of the whole line. Thanks for watching.