 Lucy and in this video we're going to look at how to find the equation of the straight line that passes through two points. You should already know how to find the gradient and all about the y equals mx plus c equation but if you forgotten watch these two videos first. So we want to find the equation of the line that passes through these two points. So we start by finding the gradient of the line. We have our standard gradient equals rise over run or change in y over change in x equations or there is another really simple equation we can use y2 minus y1 divided by x2 minus x1 which is just the difference between y values divided by the difference between the x values. Choose one of the set of coordinates to be the ones and the other coordinates to be the twos. I'm going to make the four three my ones and the seven nine my twos. So then the gradient is just nine minus three divided by seven minus four which gives us six divided by three. So the gradient is two or you could just stick to the rise divided by the run six divided by three is two. So now using the y equals mx plus c format we already know the gradient m is two and we just need to find the y intercept. We could just look back at the graph and see that the y intercept is negative five so the equation be y equals 2x minus five. But you won't always have the graph the question could look like this. So let's have a look to see how we'd find the y intercept with this question. So we know our gradient is two and with our y equals mx plus c equation we have y equals 2x plus c. To find the missing y intercept c value use one of the sets of coordinates that was given to us in the question. So four three or seven nine. I'm going to use four three. So when x is four y is three and just substitute these values into our equation y equals 2x plus c. So instead of y we have three and instead of x we have four. So now we have three equals two multiplied by four plus c. So three equals eight plus c. We arrange by subtracting eight from both sides and we get c equals negative five. So the gradient m was two. The y intercept is negative five. So our equation is y equals 2x minus five. So there really wasn't much more to learn. Just that nice simple gradient equation y two minus y one divided by x two minus x one. It doesn't really matter which set of coordinates you make your twos and which ones you make your ones. They both work. In part two we're going to look at another example for you to do yourself. There won't be a graph involved so you've got to use all the equations.