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Equation of the Tangent line With no points


aimforthehead
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I'm reviewing a calculus test I took and ran into this problem, which I got right but don't remember how...

Find the equation of the tangent line to the curve y = f(x) which is parallel to the line 3x - 4y = 1

y = 3/4x - 1/4

So my answer was

y = 3/4x + 5/4, where did the 5/4 come from? Without points how can we find what b is? Or am I missing information from the problem you think?

Thanks.

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aimforthehead - these sorts of situations it is very useful to draw a quick sketch. It might show you two things that as mathematic keeps telling you - the question is incomplete (you need at least one point on the line y=f(x). There are an infinite number of curves that are tangent to a line parallel to your function.

 

Talking about tangents to straight lines is also a little weird as well - the tangent to a straight line is the line itself; we normally refer to tangents when talking about actual curves, the tangent is the line that touches the curve and thus has the same instantaneous slope as the curve at that point.

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  • 1 month later...

I'm reviewing a calculus test I took and ran into this problem, which I got right but don't remember how...

Find the equation of the tangent line to the curve y = f(x) which is parallel to the line 3x - 4y = 1

y = 3/4x - 1/4

So my answer was

y = 3/4x + 5/4, where did the 5/4 come from? Without points how can we find what b is? Or am I missing information from the problem you think?

Thanks.

Wait, f(x)=y? That would mean the derivative is always 3/4. Unless you mean f'(x) or f''(x) is 3/4x-1/4, there shouldnt be a curve.

Edited by SamBridge
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  • 2 weeks later...

The idea is that f(x) is some curve such that at some point on the curve, the tangent is parallel to the (otherwise unrelated) line 3x - 4y = 1 => y = (3/4)x - 1/4. As imatfaal has directly and mathematic has indirectly pointed out, there are infinitely many curves that have this property. Therefore, the answer to the OP's question depends on what, exactly, f(x) is.

Edited by John
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I'm reviewing a calculus test I took and ran into this problem, which I got right but don't remember how...

Find the equation of the tangent line to the curve y = f(x) which is parallel to the line 3x - 4y = 1

y = 3/4x - 1/4

So my answer was

y = 3/4x + 5/4, where did the 5/4 come from? Without points how can we find what b is? Or am I missing information from the problem you think?

Thanks.

From the looks of it, anything about f(x) or tangents is extraneous. You were actually only asked to find an equation of a line that is parallel to another line. By changing nothing more than the y intercept on the given line equation, you found "the equation of the...line..parallel to the line...". It sounds like a trick question designed to test your reading comprehension, which you got correct. You could have substituted any number in place of 1/4.

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