proof of y2-y1/x2-x1

I know you use this formula to work out the gradient.
(5 , 7) (6, 8)
Here you would do (8-7)/(6-8) to get a 1/2 as the gradient, but i don't understand how this formula gets me the answer? If you are a good mathematician help me please, I really want to understand what I'm doing rather than just doing it for no reason.

I know you use this formula to work out the gradient.
(5 , 7) (6, 8)
Here you would do (8-7)/(6-8) to get a 1/2 as the gradient, but i don't understand how this formula gets me the answer? If you are a good mathematician help me please, I really want to understand what I'm doing rather than just doing it for no reason.

The gradient of a straight line is the change in the y-value per change in x by 1. Dividing the change in y by the change in x gives you this value.

i feel that like that is the actual(one of many) definitions of the gradient

i mean if you want to see for yourself i guess you could look at the graph but then when you think gradient you'll think the slope of the line(when you connect 2 points) is the gradient. Working it out is essentially simple.

https://www.mathsisfun.com/definitions/gradient.html
This one says that the gradient is how steep a line is so ye...

yee i know how to calculate gradient (steepness), i just wanted the proof, or understanding of how you would use (y2-y1)/(x2-x1) to calculate it.
Its change in y over change in x.