Question

Pre-Calculus question, picture posted. Determining secant equation.

Answer 1

The first one. Altho Im not sure what they want in the second one either. I don't really understand what the question is asking of me.

Answer 2

so, you want to define a line between 2 points ....

Answer 3

a general point A is defined by f(x)=4^x as 4^A .... right?

so we would simply need to define the slope of the line from 4^2 to 4^A, then use the point slope form to define the equation of that line

Answer 4

so I got f(a)-f(2) divides by a-2

Answer 5

wouldthat be the equation?

Answer 6

good, and lets use the point they establish for us as (2,4^2)

Answer 7

thats not the equation, just the slope of the line between the points

Answer 8

so I have to integrate something to solve for b?

Answer 9

\[y=\frac{4^A-4^2}{A-2}(x-2)+4^2\]

Answer 10

you dont have to integrate anything to find a derivative .... unless thats some method that your marterial has asked you to do

Answer 11

ohhhh u got the line, figured out thetransformations, and then put them into the equation

Answer 12

yep ...

Answer 13

how did u get the transformations

Answer 14

\[slope=\frac{f(b)-f(a)}{b-a}~:~let f(x)=4^x,~and~b=A~and~a=2\]

Answer 15

\[slope-point:y=m(x-h)+k~:~text{for some (h,k) point}\]

Answer 16

the reply isnt formating my coding .. so i cant tell when i mess up :)

Answer 17

im trying to follow u on paper

Answer 18

the secant line (a line between 2 points on the same curve) is therefore given to be:\[y=\frac{4^A-4^2}{A-2}(x-2)+4^2\]

Answer 19

i tried plugging in 2 and 16 and got 16=2m-mh+K

Answer 20

recall that A is some general value ....

Answer 21

i still dunno how u gotx-2 or +16

Answer 22

they give us that information in the setup: use (2,f(2)) to establish your setup

Answer 23

i know they are trasnformations up and sideways

Answer 24

man i feel stupid i still dont understand the lastpart:S

Answer 25

lol sorry

Answer 26

spose they asked a more basic question, which is really all that this amounts too, as:

given a slope 5 and a point (2,1) what is the equation of the line in point-slope format?

Answer 27

1=10+b
b=-9

Answer 28

y=5x-9

Answer 29

thats slope-INTERCEPT format ... not point-slope format; even tho it ends up being a correct equation for the line

Answer 30

when given a slope (m) and a point (h,k); we can construct a line to be defined as:

y-k = m(x-h) or written another way: y = m(x-h) + k

Answer 31

the information in the question supplies is with a slope to determine; and give us a point to use

Answer 32

\[slope:\frac{4^A-4^2}{A-2}\]\[point:(2,4^2)\]

Answer 33

ohhhhhhhhhhhhhhhhhhh

Answer 34

clicked! THANK U

Answer 35

:) then it asks you how you could use this setup to determine the equation for the slope at a single point

Answer 36

lol since ur here anyways u know the second question>