Normal and Parallel Lines

In summary, the problem asks to find an equation of a line that is both normal to the graph y=2x/(x-1) and parallel to the line 2x-y+1=0. The solution involves finding the slope of the given line and using it to find the slope of the normal line. The normal line's slope is then set equal to the slope of the given line to find the point(s) at which the normal is parallel to the given line. The solution requires finding the derivative of y=2x/(x-1) and solving for x.
  • #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
 
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  • #2
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?
 
  • #3
Use the concept of slope to solve this.
 
  • #4
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
hmmm maybe by parallel they are referring to a tangent line?...well...maybe lol :smile:
 
  • #6
ashleyk said:
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.
 
  • #7
ashleyk said:
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
 
Last edited:

1. What is the difference between normal and parallel lines?

Normal lines are those that intersect at a 90-degree angle, also known as perpendicular lines. Parallel lines, on the other hand, are lines that never intersect and maintain the same distance between them at all points.

2. How can you determine if two lines are parallel?

Two lines are parallel if they have the same slope. This means that their steepness or incline is equal. Another way to determine parallel lines is by using the slope-intercept form of the equation, where the slopes are the same but the y-intercepts are different.

3. Can normal lines also be parallel?

No, normal lines cannot be parallel because they intersect at a 90-degree angle. Parallel lines, by definition, do not intersect at any point. However, normal lines can be perpendicular to parallel lines.

4. How are normal and parallel lines used in real life?

Normal and parallel lines are used in many fields, such as architecture, engineering, and mathematics. In architecture, normal and parallel lines are used to create structures that are strong and stable. In engineering, they are used to design roads, bridges, and buildings. In mathematics, normal and parallel lines are used to solve equations and analyze geometric shapes.

5. How can you draw normal and parallel lines?

To draw normal lines, you will need a protractor to measure a 90-degree angle. Place the protractor at the point where the lines will intersect and draw a line at the designated angle. To draw parallel lines, you can use a ruler and measure equal distances from the original line to create the parallel lines.

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