# Equation for line tangent to curve

• Sep 22nd 2009, 09:02 PM
asweet1
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.
• Sep 22nd 2009, 09:13 PM
Chris L T521
Quote:

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 $\displaystyle \frac{\,dy}{\,dt}$ at $\displaystyle t=2$. This will be your $\displaystyle m$.

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

$\displaystyle y-y_0=m(x-x_0)$

Can you take it from here?
• Sep 22nd 2009, 09:18 PM
asweet1
• Sep 22nd 2009, 09:28 PM
Chris L T521
Quote:

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.

Quote:

Originally Posted by asweet1

That is not correct.

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

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

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

$\displaystyle y-80=70(x-2)$

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

Does this make sense?
• Sep 22nd 2009, 09:29 PM
mr fantastic
Quote:

Originally Posted by asweet1

No.

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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