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Help with secant line

  1. Oct 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the slope of the line that joins P (0,2) and Q (x, 2^x+1) for x ≠0. type the expression using x as a variable.


    2. Relevant equations
    Rise over Run?



    3. The attempt at a solution
    I have a picture of the graph but i don't really know what to do, Please help.
    I graphed it at x= -3, -2 and -1 cause that was part 1
    Okay so i just had a thought in my mind. So we can use limits to find the slope of the secant line, So would i use The limit of 2^x+1 as x approaches 0. But then the slope would be 1, And how would i write the expression in terms of x.
    So for when x=-1 the rise/run is .5/1
    x=-2 rise over run is .75/2
    and when x=-3 rise over run is .875/3
    but now how would i do the expression part?
     

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    Last edited: Oct 4, 2012
  2. jcsd
  3. Oct 4, 2012 #2

    jedishrfu

    Staff: Mentor

    need to show some work, why not compute the slope as you said rise over run
     
  4. Oct 4, 2012 #3
    Just rewrite Q (x, 2^x+1) as Q(x)=2^x+1 and find your secant line at that point.
     
    Last edited: Oct 4, 2012
  5. Oct 4, 2012 #4

    SammyS

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    Given two points on a line, do you know how to get the slope?
     
  6. Oct 4, 2012 #5
    So for when x=-1 the rise/run is .5/1
    x=-2 rise over run is .75/2
    and when x=-3 rise over run is .875/3
    but now how would i do the expression part?
     
  7. Oct 4, 2012 #6

    SammyS

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    Now find the slope for the line passing through points (0,2) and (x, 2x+1 )

    Yes, there will be a variable involved.
     
  8. Oct 5, 2012 #7
    couldn't i just use the limit of 2^x+1 as x approaches 0 to find the slope?
     
  9. Oct 5, 2012 #8

    SammyS

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    The slope of what?
     
  10. Oct 5, 2012 #9
    the slope of the secant line
     
  11. Oct 5, 2012 #10
    doesn't the secant line connect those 2 points, so cant i figure out the slope using limits
     
  12. Oct 5, 2012 #11

    SammyS

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    You don't need to take any limits. You're finding the slope of a line, given two distinct points, one of which has coordinates given in terms of x.
     
  13. Oct 5, 2012 #12
    Thanks a lot for the help.
    the answer was 2^x-1/x.
     
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