1. ## equations of lines

hi,

i need to find the equation of this line, perpendicular to y=2x and passing through (0,0)

im not too sure how to work this out so i require some help please!!

thanks!

2. ## Re: equations of lines

Originally Posted by andyboy179
hi,

i need to find the equation of this line, perpendicular to y=2x and passing through (0,0)

im not too sure how to work this out so i require some help please!!

thanks!
The product of the slopes of perpendicular lines is always -1.

3. ## Re: equations of lines

what does that mean?

4. ## Re: equations of lines

Originally Posted by andyboy179
what does that mean?
It means if you were to multiply the two slopes of your lines together, you would get -1. You (should) already know one of the slopes...

5. ## Re: equations of lines

what are the two slopes?? is it (0,0)?

6. ## Re: equations of lines

Originally Posted by andyboy179
what are the two slopes?? is it (0,0)?
No, the slope of the line represents the rate at which y changes per unit change in x. For a linear equation of the form y = mx + c, the slope/rate is equal to the value of m. The y-intercept is c...

So what is the slope of your original line?

slope=2

8. ## Re: equations of lines

Originally Posted by andyboy179
slope=2
Yes, so what is the slope of the other line, keeping in mind that the two slopes need to multiply to -1...

9. ## Re: equations of lines

theres another slope? where is -1 coming from?? i really don't understand what you are saying.
so would i do this y=2x+c, 2 is the slope?

10. ## Re: equations of lines

Originally Posted by andyboy179
theres another slope? where is -1 coming from?? i really don't understand what you are saying.
so would i do this y=2x+c, 2 is the slope?
Andy, do you not have a math teacher?
If so, any idea why he/she would give you this problem, and not explain slopes?

11. ## Re: equations of lines

yes i do have a maths teacher, she has explained it however we havent made notes on it and i don't understand it, and its hard because we have a class with about 70 kids in it so she can't see everyone at once, i shall ask for information from her after the week end.

12. ## Re: equations of lines

Originally Posted by andyboy179
...however we havent made notes on it...

13. ## Re: equations of lines

??
year11, my final year, i've completed my GCSE in maths and im now doing additional maths

14. ## Re: equations of lines

Originally Posted by andyboy179
??
year11, my final year, i've completed my GCSE in maths and im now doing additional maths
Oh boy...ok, Andy, I'll temporarily believe that you're in a class of 70 (outch!) plus you have a
teacher that does not allow students to take notes...
SLOPES
======
The slope of line2 perpendicular to line1 is the reciprocal of line1's slope, multiplied by -1.

This simply means you "flip over" the fraction representing line1's slope, and change its sign:
"change its sign" means change to - if it was a +, change to + if it was a -.

Keep in mind that ALL numbers are fractions: like 3 is a fraction: 3/1 ;
the /1 is implied (not shown).

So if line1 has slope of +5, then line2 will have slope of -1/5:
flip over +5/1 to get +1/5, change sign: -1/5.

Here's a few examples, Line2 being perpendicular to line1:
Code:
Line1    Line2
7       -1/7
63       -1/63
-7        1/7
-63       1/63
1/7       -7
1/63      -63
2x/y      -y/(2x)
-(2x+y)   1/(2x+y)
pi        -1/pi
Now give copies of this to your 70 classmates...and don't tell the teacher !

15. ## Re: equations of lines

Originally Posted by Wilmer
Oh boy...ok, Andy, I'll temporarily believe that you're in a class of 70 (outch!) plus you have a
teacher that does not allow students to take notes...
SLOPES
======
The slope of line2 perpendicular to line1 is the reciprocal of line1's slope, multiplied by -1.

This simply means you "flip over" the fraction representing line1's slope, and change its sign:
"change its sign" means change to - if it was a +, change to + if it was a -.
Because, as was mentioned, the two slopes multiply together to give -1.

In other words, if we call $\displaystyle \displaystyle m_1, m_2$ the slopes of the two perpendicular lines, then

\displaystyle \displaystyle \begin{align*} m_1 m_2 &= -1 \\ m_2 &= -\frac{1}{m_1} \end{align*}

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