Question

What formula is used to find the rate of change if data is given?

Answer 1

average rate of change?

Answer 2

dy/dx

Answer 3

yes that would work for instantaneous change, for average change you could use the difference quotient

Answer 4

\[\frac{f(x+h)-f(x)}{h}\]

Answer 5

Thanks @rickjbr

Answer 6

yw

Answer 7

We'd need a regression to find dy/dx using only data. For everything else there's mastercard, I mean, average change.

Answer 8

So just to clarify on the formula above where would i plug in the data? Sorry to bug = [

Answer 9

lets say I had the points (1,3) and (2,5) for my data. The slope would be (5-3)/(2-1), where (2-1)=h, and 5=f(x+h), and 3=f(x)

Answer 10

So the slope would be 2/1? Right?

Answer 11

in that example, yes

Answer 12

For the example I gave? Yeah.

Answer 13

sweet! so where would i get my y intercept to create the y=mx+b?

Answer 14

i know that x = 2/1 but b?

Answer 15

i meant i know that 2 = m

Answer 16

If you have a datapoint (x,y), you can just plug in x and y in y=mx+b, where we know m from the previous example. So solve for b, and you're set!

Answer 17

solve for b by plugging results into point slope formula?

Answer 18

Yeah.

Answer 19

is the answer \[y=2x-5\]?

Answer 20

No, unless I'm doing something wrong, it should be y=2x+1.

Answer 21

i'm wrong...

Answer 22

you're wrong?