Slopes of Secants and Average Rate of Change

Average rates of change are like a mixture of Physics and a little basic maths. It's basically the y-values divided by its x-values.  In other words, it is like the gradient/slope of any graph with respect to its x-values.

Let's just say...

A circular wave is formed on the surface of a basin filled with water. The table below shows the radius of the circular wave during the first 10s.

Time, t (s)	Radius, r (m)
0	0
1	2
2	4
3	6
4	8
5	10
6	12
7	14
8	16
9	18
10	20

If a question asks, determine the average rate of change of the radius, this means,

∆ y ÷ ∆ x = yx^-1

in this case, the specific formula would be... 

∆ r ÷ ∆ t = rt^-1

then,

(20 - 0) m ÷ (10 - 0) s = 2ms^-1

Note:

- Secant is the name for the line on a graph which connects ANY TWO points on a graph ; be it a quadratic graph, cubic graph or what not.

- Remember to have the x value written with a power of negative 1 (the small -1 on the top of it) or the answer will have no meaning

This part of math is just about UNDERSTANDING its formula, NOT memorizing it, but spending time to PRACTISE on it. I've found a pretty useful website that gives you examples and its solutions as well as some necessary explanation. Check it out Here!

Until next time!~