# Equation of tangent line.

#### cgr4

##### New member
The line y = ax + b is tangent to y=x3 at the point P = (-3,-27). Find a and b.

I'm pretty lost on this one.

Here's my initial thoughts. Find (a) first.

(a) is equal to the slope which is the derivative of x3

So (a) would be equal to 3(-3)2 ?

Not quite sure where to start on this one.

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
The line y = ax + b is tangent to y=x3 at the point P = (-3,-27). Find a and b.

(a) is equal to the slope which is the derivative of x3

So (a) would be equal to 3(-3)2 ?
Yes. Once you know $a$, $y=-27$ and $x=-3$, it is easy to find $b$.

#### cgr4

##### New member
Yes. Once you know $a$, $y=-27$ and $x=-3$, it is easy to find $b$.
so a = 27

so, y = 27(-3) + b

-27 = -81 + b

therefore b = 64?

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
-27 = -81 + b

therefore b = 64?
Correct, except that 81 - 27 = 54.