How do you convert from one line equation to another?

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Homework Help Overview

The discussion revolves around converting the equation of a line from the form y-2=4x-4 to the equivalent form 4x+y-6=0. Participants are exploring the validity of this conversion and its implications in the context of finding a tangent line to a circle.

Discussion Character

  • Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Some participants attempt to manipulate the original equation to find an equivalent form, while others question the equivalence of the two equations. There is also a discussion about the method of finding the slope of the tangent line to a circle using implicit differentiation.

Discussion Status

The discussion is active, with participants providing insights into the conversion process and the derivative calculation for the tangent line. Some guidance has been offered regarding the steps to find the slope and the tangent line equation, although there is no explicit consensus on the equivalence of the line equations.

Contextual Notes

Participants are working under the constraints of homework rules, and there is a focus on understanding the relationship between the line equation and the tangent to the circle at a specific point.

Andy21
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Homework Statement



Show how the equation of a line y-2=4x-4 can be converted into the equivalent line equation of 4x+y-6=0.

Homework Equations





The Attempt at a Solution



The closest I have got to it is 4x-y-2=0 by adding and subtracting terms to both sides.
 
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Andy21 said:

Homework Statement



Show how the equation of a line y-2=4x-4 can be converted into the equivalent line equation of 4x+y-6=0.
It can't. These two equations aren't equivalent.

y - 2 = 4x - 4
<==> y - 4x + 2 = 0
I got this by adding -4x and +4 to both sides.
This equation is equivalent to the one you show below. Multiply the equation above by -1 on both sides and you'll get an equation that can be rearranged to yours.
Andy21 said:

Homework Equations





The Attempt at a Solution



The closest I have got to it is 4x-y-2=0 by adding and subtracting terms to both sides.
 
Thanks for the help. The reason I asked this question is to find the equation of the tangent to the circle (x+3)^2 + (y-1)^2=17 at the point (1,2). I know the answer to this is 4x+y-6=0. Can you explain to me how to get this answer.
 
That answer is correct. I think you made a mistake in calculating the derivative. The slope of the tangent line at (1, 2) is -4, not 4, as you show.
 
Yes sorry, what I asked in the original question was wrong. Can you explain how to get the answer 4x+y-6=0 for the equation of the tangent from the circle equation and the point I gave in my previous reply. Thanks.
 
1. Find dy/dx using the circle equation. I used implicit differentiation.
2. Evaluate dy/dx at (1, 2) to get the slope of the tangent line.
3. Use the slope found in step 2 and the point (1, 2) in the point slope form of the line.
 

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