Find the average rate of change for f(x)=10x+3 over the interval [1,8]. be sure to simplify the answer. explain how you did it

Step-by-step explanation:

rate of change is how fast it changes, so think of it like looking at average speed.  If a car moves so the distance is shown by that equation then at second 1 it is 10(1)+3 = 13 meters then at second 8 it's at 10(8)+3 = 83 what is the average speed?  well, speed is distance / time, so let's do that.  what was the change in distance, or the difference in other words.  Well, it's 83-13 = 70.  change in time is similarly 8-1 = 7  so now speed would be 70/7 = 10.  So that's the rate of change.

Look though, in the equation we have 10x.  Things would be different if it wasn't just x, but since it is we can really easily find the rate of change  by looking at the number  next to x.  If it were something else, or inside a set of parenthesis it wouldn't be this simple.  

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.