Equation for tangent to a curve and parallel to another line

Thread starter QUITE RIGHT
Start date Oct 7, 2009
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Curve Line Parallel Tangent

In summary, the equation for a tangent to a curve and parallel to another line is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope of a curve at a specific point, you can use the derivative of the equation of the curve. The slope of the tangent line at a specific point is equal to the slope of the curve at that point and a curve can have only one tangent line at a specific point. To find the equation of a parallel line, you can use the fact that parallel lines have the same slope and find the y-intercept using the point where the parallel line intersects the curve.

Oct 7, 2009

QUITE RIGHT

How would find the equation of a line that has to be tangent to a curve and parallel to another line (i know slope has to be equal)

(you are given the equation of the line and the curve)
x^3
3x-y-6

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Oct 8, 2009

LCKurtz

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What equations? Where are the equations? You don't have any equal signs. State the problem correctly and show us what you have tried.

FAQ: Equation for tangent to a curve and parallel to another line

What is the equation for a tangent to a curve and parallel to another line?

The equation for a tangent to a curve and parallel to another line is y = mx + b, where m is the slope of the line and b is the y-intercept.

How do you find the slope of a curve at a specific point?

To find the slope of a curve at a specific point, you can use the derivative of the equation of the curve. The derivative is the rate of change of the curve at that point and can be calculated using calculus.

What is the relationship between the slope of the tangent line and the slope of the curve at a specific point?

The slope of the tangent line at a specific point is equal to the slope of the curve at that point. This is because the tangent line is the best approximation of the curve at that point and thus has the same rate of change.

Can a curve have multiple tangent lines at the same point?

No, a curve can have only one tangent line at a specific point. This is because the tangent line represents the instantaneous rate of change of the curve at that point and there can only be one instantaneous rate of change.

How can you use the equation of a tangent line to find the equation of a parallel line?

To find the equation of a parallel line, you can use the fact that parallel lines have the same slope. So, if you know the slope of the tangent line, you can use it as the slope of the parallel line and find the y-intercept using the point where the parallel line intersects the curve.