Math 8 Equations Help - Please Help!

[AbhiKap]

Hello, AbhiKap here

I really need help on this problem:

Which equation describes the line that passes through the point (2, – 1) and is perpendicular to the line x - 3y = 9?

They have 4 options to choose from given and there are two that have a slope of 3. The other two do not so I cancelled them out. However, I do not know what to do next.

Thanks, Help is appreciated

 

[pka]

Which equation describes the line that passes through the point (2, – 1) and is perpendicular to the line x - 3y = 9?

Any such line has to look like
\(\displaystyle 3x+y=?\)

 

[AbhiKap]

Any such line has to look like
\(\displaystyle 3x+y=?\)

Yes, I see but there are two such lines:

3x+y=5 and also 3x+y=-5

 

[mmm4444bot]

the line x - 3y = 9

If you were to determine the slope of the line above, you could then use the Point-Slope Form to determine the equation of the perpendicular line through point (2,-1).

Do you know how to determine the slope of the line above?

 

[HallsofIvy]

Yes, I see but there are two such lines:

3x+y=5 and also 3x+y=-5

Okay you have the slope -1/3 because they are perpendicular to the given line. Now, use the other information you are given- which of those contains the point (2, – 1)?
That is, if you replace x by 2 and y by -1, what do you get?

 

[pka]

Yes, I see but there are two such lines:
3x+y=5 and also 3x+y=-5

But which of those contains \(\displaystyle (2,-1)~?\)

 

[AbhiKap]

Okay you have the slope -1/3 because they are perpendicular to the given line. Now, use the other information you are given- which of those contains the point (2, – 1)?
That is, if you replace x by 2 and y by -1, what do you get?

Ok so you mean that I should replace x and y by 2 and -1 and it should equal what is there?

 

[JeffM]

Ok so you mean that I should replace x and y by 2 and -1 and it should equal what is there?

OK. You correctly saw that the slope of the correct equation had to be 3 so you were able to reject two of the equations offered as choices. That left two equations, each with a slope of 3. What everyone is saying is that, in addition to having the correct slope, the correct equation must also be true when 2 is substituted for x and - 1 is substituted for y. So which equation is it?