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Analytic Geometry question

  1. May 21, 2014 #1
    Hey so I have a math test tomorrow and I'm really good in math, I just need some small clarification, so here's my problem.

    V(-2,k) P(4,9) slope of 2/3

    so I decided to find y=mx+b with P(4,9) because after I find B I could do the same with V(-2,k)

    so I did the equation and B came up 7, so next I decided to do.


    y=2/3(-2)+7

    but I got, y=17/3

    However in the optional choice there's only -5, 3, 5 and 7 I asked my friend and he said it was 5 but I didn't really understand his explanation so I would really appreciate some deeper or simple explanation please, my friend also told me that the way I was doing it wouldn't work and I was just wondering as to why not ?

    thank you for your time.

    ps: It may not be called a slope but I come from a french school and that was the translation I came up with.
     
  2. jcsd
  3. May 21, 2014 #2
    You got the wrong value for b. As you said [itex]y=\frac{2}{3}x+b[/itex]. If you use the first point you have:
    $$
    9=\frac{2}{3}\cdot 4+b\implies b=9-\frac{8}{3}=\frac{19}{3}.
    $$
    So [itex]y=\frac{2}{3}x+\frac{19}{3}[/itex]. Lastly, plugging x=-2:
    $$
    y=\frac{2}{3}\cdot(-2)+\frac{19}{3}=\frac{-4+19}{3}=\frac{15}{3}=5.
    $$
    I hope this is clear.
     
  4. May 22, 2014 #3

    verty

    User Avatar
    Homework Helper

    Or you could do it in one step using the point-slope formula and entering both points.
     
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