Trouble with Tangent of a Line

In summary, Mr Radou told me that the equation of the line perpendicular to the tangent at (1,5) is y - y_{1} = -\frac{1}{10}(x-x_{1}), where (x_{1}, y_{1})=(1, 5). Plugging in the values, the equation of the line is y - y_{1} = -\frac{1}{10}(x-x_{1}), where (x_{1}, y_{1})=(1, 5.1).
  • #1
thomasrules
243
0
I tried many thigns with this one:

Determine the equation of the line that is perpendicular to the tangent to [tex]y=5x^2 at (1,5)[/tex]

What I did was use the formula for instantaneous rate of change finding the equation of the secant.

[tex](5x^2-5)/(x-1)[/tex]

from there I found that the slope of the tangent is about 10 and from there I'm lost
 
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  • #2
thomasrules said:
I tried many thigns with this one:

Determine the equation of the line that is perpendicular to the tangent to [tex]y=5x^2 at (1,5)[/tex]

What I did was use the formula for instantaneous rate of change finding the equation of the secant.

[tex](5x^2-5)/(x-1)[/tex]

from there I found that the slope of the tangent is about 10 and from there I'm lost

Maybe it would be easier to differentiate the function and plug in the x-coordinate to find the slope of the tangent.
 
  • #3
but I have the slope...
 
  • #4
thomasrules said:
but I have the slope...

Ok then. In what relation are the slope of a line with the slope of a line perpendicular to it?
 
  • #5
duh negative reciprocal
 
  • #6
thomasrules said:
duh negative reciprocal

So, all you have to do now is find the equation of the line which passes through the given point and whose slope is, as you stated, negative reciprocal to the slope of the tangent at that very same point.
 
  • #7
answer is x+10y-51=0 but whres the 51 from
 
  • #8
thomasrules said:
answer is x+10y-51=0 but whres the 51 from

The equation of the line is [tex]y - y_{1} = -\frac{1}{10}(x-x_{1})[/tex], where [tex](x_{1}, y_{1})=(1, 5)[/tex]. Plug in the values and you should get the equation. (And see where 51 comes from.)
 
  • #9
ur not suggesting y-y1=m(x-x1)

??
 
  • #10
thats what i did one sec
 
  • #11
omg I'm so smart because I got to that last step u said but didnt see that 1/10 +5 is 5.1...

but that's why I'm so stupid too i didnt see it
 
  • #12
thomasrules said:
omg I'm so smart because I got to that last step u said but didnt see that 1/10 +5 is 5.1...

but that's why I'm so stupid too i didnt see it

You're not stupid, you're just slumpy. That can be cured easily. :smile:
 
  • #13
Thank you Mr Radou for your help and compliment
 

FAQ: Trouble with Tangent of a Line

What is the definition of the tangent of a line?

The tangent of a line is a mathematical concept that represents the ratio of the length of the side opposite to an acute angle in a right triangle to the length of the adjacent side.

How do you calculate the tangent of a line?

The tangent of a line can be calculated by dividing the opposite side length by the adjacent side length in a right triangle, or by using a scientific calculator or trigonometric table.

Why is the tangent of a line important?

The tangent of a line is important in mathematics and physics because it helps us to understand the relationship between angles and sides in a right triangle, as well as in the graphing of functions and determining the slope of a line.

What are some common mistakes when working with the tangent of a line?

One common mistake is confusing the tangent ratio with the slope of a line. Another mistake is using the tangent function with degrees instead of radians, or vice versa.

How can I improve my understanding of the tangent of a line?

To improve your understanding of the tangent of a line, it is important to practice solving problems involving triangles and functions, and to review the definitions and properties of the tangent function. You can also seek help from a math tutor or join a study group to further discuss and clarify any questions you may have.

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