A gradient is in the very simplest of terms how
steep a
line is at a given point.
For straight lines this is nice and easy because the gradient stays the same along the whole line.
To calculate the gradient of a straight line you simply take any 2 points on that line (let’s call them A and B)and take the change in the y-axis values (how much higher or lower A is than B) and divide that value by the change in the x-axis values (how far A is left or right of B).
In other words you take delta y over delta x.
e.g. a line that went up 2 units whenever it went across (to the right) 1 unit would have a gradient of 2 {draw it and see if your not sure why}
Easy so far? Good.
For curved lines it gets a little more difficult but not much so don’t worry.
Curves do not have uniform gradients so you can’t say that a curve has the same gradient at all points on that curve but you can find the gradient of a curve at a given point on that curve.
In order to find the gradient exactly you must differentiate the curve but you can approximate the gradient as accurately as you fairly easily. All you need to do is zoom in on the bit of the curve you are interested in as you look at a smaller and smaller section of the curve it will begin to look straighter and straighter until it appears to be perfectly straight then you can find the gradient as described above. Note: Delta x and delta y will be tiny, the smaller they are the better your approximation.
If you have the line in the form of equation then all you need to do is take the point you are trying to find the gradient of as your point A and to plug a very slightly different value for x or y into the equation to find a suitable point B.