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Math Help - Equation for line tangent to curve

  1. #1
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    Equation for line tangent to curve

    Find an equation for the line that is tangent to the curve y= 10t + 15t^2 at the point (2, 80).

    I thought I coul use the formula y=mx+b but I would need another coordinate. Is there is apecific to solve a an equation for tangent line. Please help I have to many theories. Maybe im just over thinking it.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by asweet1 View Post
    Find an equation for the line that is tangent to the curve y= 10t + 15t^2 at the point (2, 80).

    I thought I coul use the formula y=mx+b but I would need another coordinate. Is there is apecific to solve a an equation for tangent line. Please help I have to many theories. Maybe im just over thinking it.
    Find \frac{\,dy}{\,dt} at t=2. This will be your m.

    With this, use the point slope form of the line:

    y-y_0=m(x-x_0)

    Can you take it from here?
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  3. #3
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    would the answer be (x-2)/(y-2)
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by asweet1 View Post
    Find an equation for the line that is tangent to the curve y= 10t + 15t^2 at the point (2, 80).

    I thought I coul use the formula y=mx+b but I would need another coordinate. Is there is apecific to solve a an equation for tangent line. Please help I have to many theories. Maybe im just over thinking it.
    Quote Originally Posted by asweet1 View Post
    would the answer be (x-2)/(y-2)
    That is not correct.

    You need to find the derivative of the function at t=2.

    y=10t+15t^2\implies\frac{\,dy}{\,dt}=10+30t. At t=2, m=\left.\frac{\,dy}{\,dt}\right|_{t=2}=10+30(2)=70.

    Thus, the equation of the tangent line at (2,80) is

    y-80=70(x-2)

    I leave it for you to simplify this and rewrite it in y=mx+b form.

    Does this make sense?
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  5. #5
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    Quote Originally Posted by asweet1 View Post
    would the answer be (x-2)/(y-2)
    No.

    1. There's no equal sign in your answer and hence no equation.

    2. The answer should have x not t.

    Go back and do what reply #2 says to do. If you don't understand the reply, please state clearly what you don't understand.
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