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Math Help - harder gradient

  1. #1
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    harder gradient

    This is the question:

    The gradient of the line joining (-1,3) to (p,q) is -2. The gradient of the line joining (p,q) to (5,2) is -1. Calculate the values of p and q

    What I have done is created two equations:

    (q-3)/(p--1)=-2
    and
    (2-q)/(5-p)=-1

    But what do I do next?
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  2. #2
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    Quote Originally Posted by Paulo1913 View Post
    This is the question:

    The gradient of the line joining (-1,3) to (p,q) is -2. The gradient of the line joining (p,q) to (5,2) is -1. Calculate the values of p and q

    What I have done is created two equations:

    (q-3)/(p--1)=-2
    and
    (2-q)/(5-p)=-1

    But what do I do next?
    You simplify the two equations:

    \frac{q-3}{p+1} = -2 \Rightarrow q-3=-2(p+1) \Rightarrow q - 3 = -2p - 2

     \Rightarrow q + 2p = 1 .... (1)

    Do similar with the other.

    Then you solve the two equations simultaneously.
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