# TANGENT???????????????????

The slope of the tangent line to the parabola y = 3 x^2 + 4 x + 2 at the point ( 2 , 22 ) is: 2

The equation of this tangent line can be written in the form y = mx+b where m is:_______________?

and where b is:_______________?

### 5 Answers

- 9 years agoFavorite Answer
Hi Fapre,

Agree with Iobo that m is the slope of the tangent line and b is the y-intercept of the tangent line. However, I would just add what the actual values are when applied to the parabola and its tangent you cited.

In this case, y' = 6x + 4 means that y'(2) = 16. So the the slope of the tangent line at x=2 is m=16.

To find b, the y-intercept of the tangent line, just use y=mx+b, your point (2,22) as (x,y), and m=16:

That gives 22 = 16(2) + b, or b = -10. Thus the equation of the tangent line to the parabola is y = 16x - 10.

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Source(s): http://www.youtube.com/watch?v=64mxT6b6qz4 http://www.dummies.com/how-to/content/how-to-find-... - Anonymous9 years ago
First, find the derivative:

dy/dx=6x+4

Now, plug in x:

dy/dx=6(2)+4=16<------this is your slope (m)

Now plug this into the y=mx+b equation given your x,y coordinates to solve for b:

22=16(2)+b

22=32+b

b=-10

So:

m is 16

b is -10

And your equation is y=16x-10

- frak1a12345Lv 69 years ago
y = mx + b is known as the "slope/intercept" form of a line equation.

m is the slope of the line and b is the y intercept of the line.

You plug in the 3 known quantities x, y and m (all are given to you) and solve for b.

- Wile E.Lv 79 years ago
y = 3x² + 4x + 2

dy/dx = 6x + 4

x = 2

y = 22

dy/dx = 6(2) + 4

dy/dx = 12 + 4

dy/dx = 16

b = y - [(dy/dx)(x)]

b = 22 - [16(2)

b = 22 - 32

b = - 10

Equation of Tangent Line:

y = 16x - 10

¯¯¯¯¯¯¯¯¯¯¯

m = 16

¯¯¯¯¯¯¯

b = - 10

¯¯¯¯¯¯¯

Source(s): 5/9/12 - How do you think about the answers? You can sign in to vote the answer.