How To Find The Gradients And Equations Of Lines

Hi. My name is Patrick McCarthy a math tutor of London today I am going to teach you math. In this video I am going to show you€”How to find the equation of a line.



The equation of a line is always-always written in the form y = mx + c this m represents the gradient of your line and this c represents the y-intercepts and I going to show you that looks like on the graph. This is what your straight line looks like. Now, you need to do is find two point on the line, two points in the line, lets say this point (1,3), (2,5), so we are going to take this point here and this point here.


Now what you need to do is find the gradient and the gradient in basically is the difference, lets give it by delta Y over delta X. The difference in the y divided by the difference in x, subsist enough toward line down from your first point to the line across your second point. This point here, this is your delta y and this is your delta x here.

And to find this we know this point here is (2,5) and this point here is (1,3), so your delta y is your change in your y, so if you take a first y value in and you take away the second y value the 5 take away 3 is divided by the change in the x, that's the 2 take away 1. So, that you putted 2 over 1 which is 2. That represents your gradient now if you get back to equation y = mx + c, m presents the gradient so we know now y is 2x + c, we still don't know what C is? But we found the gradient by looking at the gradient of a line OK.

Now, I need to find C, C presents this point here, it represents the y intercept is called is the point where the line crosses this axis in the y-axis, this is called your y intercept and this is represented by the letter C and to find out we take one point on the line, lets take this point here when we put this x value 2 and this Y value 5 into this equation, so we put 5 whether its a Y and whether its a X, so we get this 5 equal 2 times 2 plus C. So, that means that 5 equals 4 + C, fro C represents a number 5 = 4 + C, well that's means the C is 1, C=1. So, we know the equation of our line y =2X + 1; and you can see here this point here then has to be the point (0,1), when X is 0, Y is 1.

So, you put 0 in here this gives 2 time 0 and y is 1, this is your intercept and this we used to find your gradient. And that's how to find the equation of a line.
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