Normal line: $-5$ or $frac{1}{5}$?
$begingroup$
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
asked Jan 3 at 0:27
wenoweno
29211
$endgroup$
add a comment |
$begingroup$
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
asked Jan 3 at 0:27
wenoweno
29211
$endgroup$
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
add a comment |
$begingroup$
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
asked Jan 3 at 0:27
wenoweno
29211
$endgroup$
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
asked Jan 3 at 0:27
wenoweno
29211
asked Jan 3 at 0:27
wenoweno
29211
asked Jan 3 at 0:27
wenoweno
29211
asked Jan 3 at 0:27
wenoweno
29211
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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 $-5$.
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
$endgroup$
$begingroup$
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
add a comment |
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$begingroup$
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 $-5$.
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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 $-5$.
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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 $-5$.
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
$endgroup$
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 $-5$.
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
answered Jan 3 at 0:33
John DoeJohn Doe
11.2k11239
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
add a comment |
$begingroup$
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
add a comment |
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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