How to Find Equations for Lines Normal to y=2x/(x-1) and Parallel to 2x-y+1=0?

[ashleyk]

Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0

 

[HallsofIvy]

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?

 

[Pyrrhus]

Use the concept of slope to solve this.

 

[ashleyk]

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(?)

 

[Physicsisfun2005]

hmmm maybe by parallel they are referring to a tangent line?...well...maybe lol

 

[HallsofIvy]

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(?)

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.

 

[ehild]

Find an equation of each line normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0

Is it meant as shown in the attachment?

ehild