please help ... Write the equation of the line which passes through (2, –1) and is perpendicular to the line with equation 3y – x =

Question

anonymous · Answer

is this a line graph if it is follow the formula mx + b
m standing for gradient, b interception point on the y axis

anonymous · Answer

3y-x=?

anonymous · Answer

I guess you're asking for this ? :P ... http://www.okc.cc.ok.us/maustin/EquationsofLine/Equations%20of%20a%20Line.htm here's everything you want to know.

anonymous · Answer

slope of $3y-x=\text{whatever}$  is $\frac{1}{3}$ and so slope of perpendicular line must be the negative reciporcal. the negative reciprocal of $\frac{1}{3}$ is $-3$ so you know your slope is $-3$ and your point is $(2,-1)$ now use the point -slope formula 
$$y-y_1=m(x-x_1)$$ with 
$$m=-3, x_1=2, y_1=-1$$ and you should get your answer

anonymous · Answer

*negative reciprocal

anonymous · Answer

you good from there?

anonymous · Answer

u think so... -1-(-1)=-3(2-2)

anonymous · Answer

oh actually no, so lets go slow

anonymous · Answer

your equation should look like either 
(y=mx+b\) or $ax+by=c$ 
one of those two

anonymous · Answer

in the "point - slope" formula there are three numbers and two variables. the formula is 
$$y-y_1=m(x-x_1)$$
in this formula $x$ and $y$ are variables that appear in your answer.  the  numbers are $x_1, y_1, m$

anonymous · Answer

so when you make the number replacements, leave $y$ as $y$ and $x$ as $x$ and replace only the $m$ the $x_1$ and the $y_1$ by numbers

anonymous · Answer

you want to try it or do you want me to write it. your choice

anonymous · Answer

i want to try it but i  am still confused... so x= 2, y= -1

anonymous · Answer

yes your point is $(2,-1)$ so replace $x_1$ by 2, replace $y_1$ by -1, and replace $m$ by -3
in the formula $y-y_1=m(x-x_1)$ 
leave the $y$ as $y$ and the $x$ as $x$

anonymous · Answer

can you wright it out :/

anonymous · Answer

3x-y=2?

anonymous · Answer

$$y-y_1=m(x-x_1)$$
$$y-(-1)=-3(x-2)$$ now there is some algebra to be done.
notice that i left the $x$ and $y$ exactly where they were, and only replaced the $m, x_1$ and $y_1$

anonymous · Answer

is it clear how i got that?  we knew the three numbers $m=-3, x_1=2, y_1=-1$ and replaced them in the formula

anonymous · Answer

yes

anonymous · Answer

ok good. now there is some algebra to to before you are done
first of all 
$$y-(-1)=-3(x-2)$$ then 
$$y+1=-3(x-2)$$ then distributive property
$$y+1=-3x+6$$ then subtract 1 to get 
$$y=-3x+5$$

anonymous · Answer

if you want it in the other form write it as 
$$3x+y=5$$

anonymous · Answer

thank you ! im printing all of these explinations off to help myself and friends