The equation of a straight line problems

  • #1

Homework Statement


Find the equations of two lines through A. one parallel and the other perpendicular to the line defined by the given equation.
[tex]A(-1,1),y=1[/tex]


Homework Equations


Parallel lines
[tex]y = mx + b[/tex]
then solve for b
Perpendicular
[tex]y = -mx + b[tex]
then solve for b

The Attempt at a Solution



Parallel:
[tex]y=1[/tex]
[tex]y = 0 + b[/tex]
[tex]1 = 0 + b[/tex]
[tex]b = 1[tex]
thus,
[tex]y=1[/tex]


Perpendicular:
I got stuck at the perpendicular part.... because the answer from the back of my book is x = -1

My answer is y = 1 also
 

Answers and Replies

  • #2
To get a perpendicular line, you need to swap the slopes (m) for their negative recipricol.

Example:

[tex]y=2x+5[/tex]

is perpendicular to [tex]y=-\frac{1}{2}x+5[/tex]

parallel you just change the b.

I don't know if this helps, I hope it does.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
966

Homework Statement


Find the equations of two lines through A. one parallel and the other perpendicular to the line defined by the given equation.
[tex]A(-1,1),y=1[/tex]


Homework Equations


Parallel lines
[tex]y = mx + b[/tex]
then solve for b
Perpendicular
[tex]y = -mx + b[tex]
then solve for b

The Attempt at a Solution



Parallel:
[tex]y=1[/tex]
[tex]y = 0 + b[/tex]
[tex]1 = 0 + b[/tex]
[tex]b = 1[tex]
thus,
[tex]y=1[/tex]


Perpendicular:
I got stuck at the perpendicular part.... because the answer from the back of my book is x = -1

My answer is y = 1 also
?? do you mean you get y= 1 for a parallel and a perpendicular? Surely that can't be possible!


You write:
Parallel lines
[tex]y = mx + b[/tex]
then solve for b
Perpendicular
[tex]y = -mx + b[tex]
then solve for b
That's incorrect. A line perependicular to y= mx+ b has slope -1/m, not -m. Since for y= 1, m= 0, -1/m does NOT exist. What does that tell you?

Rather than trying to plug numbers in to formulas, think! What does the line y= 1 look like? What would a line perpendicular to it look like?
 
  • #4
1,235
1
y = 1 is a horizontal line with slope 0. the perpendicular line will be vertical. what does that tell you about the slope?
 
  • #5
the slope will be -1?

but x is 0 in y = 0x + 1? could it be that the slope cant be change?
 
  • #6
1,235
1
the slope of a vertical line is undefined.
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,847
966
the slope will be -1?

but x is 0 in y = 0x + 1? could it be that the slope cant be change?
No, x is NOT 0 in "y= 0x+ 1"! The COEFFICIENT of x is 0. x can be any value.

As Courtigrad pointed out, a vertical line does not have a slope. That was my point before. In fact, my other point was that you shouldn't be worrying about 'slope' at all! y= 1 is a horizontal line. Any line parallel to it must also be a horizontal line, of the form y= constant. Of course, that means it has slope 0 but that is not really important and confuses the issue with "perpendicular" lines. Vertical lines cannot be written in the form y= mx+ b! Obviously any line perpendicular to a horizontal line is vertical. What does the equation of any vertical line look like? What must the equation of a vertical line through (-1, 1) be?
 

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