Normal line: $-5$ or $frac{1}{5}$?












1












$begingroup$


Find the equation of the normal line to the graph of $f$, $f(x) = ln(x + 1)$, so that the normal line is parallel to the line $y = −5x + 101$.



Here's the formula for finding normal line:
$y - y_{0} = frac{-1}{f'(x_{0})}(x-x_{0})$



I am simply wondering: when considering the coefficient $frac{-1}{f'(x_{0})}$, should I treat it as $-5$ or $frac{1}{5}$? $-5$ seemed obvious to me, because it's parallel to $y=-5x+101$, but I'm not sure if I'm right.



Thanks!






real-analysis calculus linear-algebra derivatives







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    You are right..
    $endgroup$
    – Ethan Bolker
    Jan 3 at 0:29






  • 3




    $begingroup$
    You’re correct. The slope must match up with the slope of the line if it’s parallel.
    $endgroup$
    – rb612
    Jan 3 at 0:30










  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38
















1












$begingroup$


Find the equation of the normal line to the graph of $f$, $f(x) = ln(x + 1)$, so that the normal line is parallel to the line $y = −5x + 101$.



Here's the formula for finding normal line:
$y - y_{0} = frac{-1}{f'(x_{0})}(x-x_{0})$



I am simply wondering: when considering the coefficient $frac{-1}{f'(x_{0})}$, should I treat it as $-5$ or $frac{1}{5}$? $-5$ seemed obvious to me, because it's parallel to $y=-5x+101$, but I'm not sure if I'm right.



Thanks!






real-analysis calculus linear-algebra derivatives







share|cite|improve this question









$endgroup$








  • 2




    $begingroup$
    You are right..
    $endgroup$
    – Ethan Bolker
    Jan 3 at 0:29






  • 3




    $begingroup$
    You’re correct. The slope must match up with the slope of the line if it’s parallel.
    $endgroup$
    – rb612
    Jan 3 at 0:30










  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38














1












1








1





$begingroup$


Find the equation of the normal line to the graph of $f$, $f(x) = ln(x + 1)$, so that the normal line is parallel to the line $y = −5x + 101$.



Here's the formula for finding normal line:
$y - y_{0} = frac{-1}{f'(x_{0})}(x-x_{0})$



I am simply wondering: when considering the coefficient $frac{-1}{f'(x_{0})}$, should I treat it as $-5$ or $frac{1}{5}$? $-5$ seemed obvious to me, because it's parallel to $y=-5x+101$, but I'm not sure if I'm right.



Thanks!






real-analysis calculus linear-algebra derivatives







share|cite|improve this question









$endgroup$




Find the equation of the normal line to the graph of $f$, $f(x) = ln(x + 1)$, so that the normal line is parallel to the line $y = −5x + 101$.



Here's the formula for finding normal line:
$y - y_{0} = frac{-1}{f'(x_{0})}(x-x_{0})$



I am simply wondering: when considering the coefficient $frac{-1}{f'(x_{0})}$, should I treat it as $-5$ or $frac{1}{5}$? $-5$ seemed obvious to me, because it's parallel to $y=-5x+101$, but I'm not sure if I'm right.



Thanks!






real-analysis calculus linear-algebra derivatives




real-analysis calculus linear-algebra derivatives






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 3 at 0:27









wenoweno

29211




29211








  • 2




    $begingroup$
    You are right..
    $endgroup$
    – Ethan Bolker
    Jan 3 at 0:29






  • 3




    $begingroup$
    You’re correct. The slope must match up with the slope of the line if it’s parallel.
    $endgroup$
    – rb612
    Jan 3 at 0:30










  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38














  • 2




    $begingroup$
    You are right..
    $endgroup$
    – Ethan Bolker
    Jan 3 at 0:29






  • 3




    $begingroup$
    You’re correct. The slope must match up with the slope of the line if it’s parallel.
    $endgroup$
    – rb612
    Jan 3 at 0:30










  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38








2




2




$begingroup$
You are right..
$endgroup$
– Ethan Bolker
Jan 3 at 0:29




$begingroup$
You are right..
$endgroup$
– Ethan Bolker
Jan 3 at 0:29




3




3




$begingroup$
You’re correct. The slope must match up with the slope of the line if it’s parallel.
$endgroup$
– rb612
Jan 3 at 0:30




$begingroup$
You’re correct. The slope must match up with the slope of the line if it’s parallel.
$endgroup$
– rb612
Jan 3 at 0:30












$begingroup$
I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
$endgroup$
– weno
Jan 3 at 0:38




$begingroup$
I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
$endgroup$
– weno
Jan 3 at 0:38










1 Answer
1






active

oldest

votes


















2












$begingroup$

Yes, $-5$ is correct - parallel lines do not intersect, and this can only happen if they have the same slope / gradient. It would be $frac15$ if you were asked to find a line that is perpendicular to the line with slope $-5$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38






  • 2




    $begingroup$
    @weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
    $endgroup$
    – John Doe
    Jan 3 at 0:47













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1 Answer
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1 Answer
1






active

oldest

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active

oldest

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active

oldest

votes









2












$begingroup$

Yes, $-5$ is correct - parallel lines do not intersect, and this can only happen if they have the same slope / gradient. It would be $frac15$ if you were asked to find a line that is perpendicular to the line with slope $-5$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38






  • 2




    $begingroup$
    @weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
    $endgroup$
    – John Doe
    Jan 3 at 0:47


















2












$begingroup$

Yes, $-5$ is correct - parallel lines do not intersect, and this can only happen if they have the same slope / gradient. It would be $frac15$ if you were asked to find a line that is perpendicular to the line with slope $-5$.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38






  • 2




    $begingroup$
    @weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
    $endgroup$
    – John Doe
    Jan 3 at 0:47
















2












2








2





$begingroup$

Yes, $-5$ is correct - parallel lines do not intersect, and this can only happen if they have the same slope / gradient. It would be $frac15$ if you were asked to find a line that is perpendicular to the line with slope $-5$.






share|cite|improve this answer









$endgroup$



Yes, $-5$ is correct - parallel lines do not intersect, and this can only happen if they have the same slope / gradient. It would be $frac15$ if you were asked to find a line that is perpendicular to the line with slope $-5$.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 3 at 0:33









John DoeJohn Doe

11.2k11239




11.2k11239












  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38






  • 2




    $begingroup$
    @weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
    $endgroup$
    – John Doe
    Jan 3 at 0:47




















  • $begingroup$
    I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
    $endgroup$
    – weno
    Jan 3 at 0:38






  • 2




    $begingroup$
    @weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
    $endgroup$
    – John Doe
    Jan 3 at 0:47


















$begingroup$
I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
$endgroup$
– weno
Jan 3 at 0:38




$begingroup$
I do have a bonus question. Basically tangent line parallel to some line is basically a normal line perpendicullar to that line? And vice-versa.
$endgroup$
– weno
Jan 3 at 0:38




2




2




$begingroup$
@weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
$endgroup$
– John Doe
Jan 3 at 0:47






$begingroup$
@weno I don't think that's right (if I am understanding correctly). A tangent line to some curve means a line that is parallel to that curve. A normal line is a line that is perpendicular to the curve. So these two things are related in this way, and are each perpendicular to each other. Does that answer what you were asking?
$endgroup$
– John Doe
Jan 3 at 0:47




















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