- #1
ashleyk
- 22
- 0
Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0
How to Find Equations for Lines Normal to y=2x/(x-1) and Parallel to 2x-y+1=0?
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Homework Help Overview
The discussion revolves around finding equations for lines that are normal to the function y=2x/(x-1) and also parallel to the line represented by the equation 2x-y+1=0. The subject area includes calculus concepts such as derivatives and the properties of normal and parallel lines.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants explore the relationship between normal lines and parallel lines, questioning whether the task involves two separate problems or a single combined requirement. There are discussions about the need to find slopes through derivatives and the implications of the normal line being perpendicular to the tangent.
Discussion Status
The discussion is active, with participants providing insights into the concepts of normal and parallel lines. Some guidance has been offered regarding the use of derivatives to find slopes, and there is an exploration of how to set up the equations based on these slopes. Multiple interpretations of the problem are being considered.
Contextual Notes
Participants are working under the assumption that the problem requires finding lines that satisfy both conditions simultaneously, and there is a mention of needing to derive slopes from the given equations.
- #2
HallsofIvy
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Why?
Could you give us some indication as to what you DO understand about these problems and what you have already tried yourself?
In particular, are these two separate problems or do you mean to find lines that are both normal to y= 2x/(x-1) AND parallel to 2x- y+ 1= 0?
Could you give us some indication as to what you DO understand about these problems and what you have already tried yourself?
In particular, are these two separate problems or do you mean to find lines that are both normal to y= 2x/(x-1) AND parallel to 2x- y+ 1= 0?
- #3
Pyrrhus
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Use the concept of slope to solve this.
- #4
ashleyk
- 22
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I understand that a normal line is perpendicular and I know what the parallel line is. I know that you have to take a derivative to get the slope. But I'm assumimg the equation must be both normal and parallel(?)
- #5
Physicsisfun2005
- 70
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hmmm maybe by parallel they are referring to a tangent line?...well...maybe lol 
- #6
HallsofIvy
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ashleyk said:
Good! Now DO it! 2x-y+1= 0 is the same as y= 2x+ 1. What is the slope of that line? What is the slope of any line parallel to that?
Find the derivative of y= 2x/(x-1) (as a function of x- you don't yet know what x is). Calling that m(x), the slope of the normal line is -1/m(x). Set that equal to the slope you got above and solve for x to find the point(s) at which the normal is parallel to 2x-y+1= 0.
- #7
ehild
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ashleyk said:
Is it meant as shown in the attachment?
ehild
Last edited: