Equation for line tangent to curve

**asweet1** · September 22nd 2009, 09:02 PM

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.

**Chris L T521** · September 22nd 2009, 09:13 PM

Originally Posted by asweet1

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?

**asweet1** · September 22nd 2009, 09:18 PM

would the answer be (x-2)/(y-2)

**Chris L T521** · September 22nd 2009, 09:28 PM

Originally Posted by asweet1

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.

Originally Posted by asweet1

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?

**mr fantastic** · September 22nd 2009, 09:29 PM

Originally Posted by asweet1

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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