# Thread: Slope of Tangent Intersecting with Line

1. ## Slope of Tangent Intersecting with Line

Determine the slope of the tangent to y=x^2+9x+9 at the point where the curve intersects the line y=3x.

The answer in the textbook is just 3. Why is this so? I don't know how they got this.

The slope of the LINE is 3. But don't I have to find the slope of the tangent? in which case I find the derivative?

I did this:

y'=2x+9
but then how did they get 3?

2. Originally Posted by john-1
Determine the slope of the tangent to y=x^2+9x+9 at the point where the curve intersects the line y=3x.

The answer in the textbook is just 3. Why is this so? I don't know how they got this.

The slope of the LINE is 3. But don't I have to find the slope of the tangent? in which case I find the derivative?

I did this:

y'=2x+9
but then how did they get 3?
first, find the point(s) of intersection ...

$x^2+9x+9 = 3x$

$x^2+6x+9 = 0$

$(x+3)^2 = 0$

$x = -3$

slope of the curve is $y' = 2x+9$ ... at the point of intersection, the slope of the curve is ...

$y'(-3) = 2(-3)+9 = 3$