Slope of Perpendicular Line to x - 3y = 9

In summary, the slope of a line perpendicular to x - 3y = 9 is -3/1. This can be found by solving for y and identifying the coefficient of x, which is the slope of the original line. The negative reciprocal of -3/1 is -1/3, which is the slope of the line perpendicular to the original line. In this case, the equation of the perpendicular line is y = -1/3x - 3. It is recommended to seek tutoring or group studying to better understand math concepts and improve grades.
  • #1
AngelShare
208
0
I don't know if I'm having a brain fart or what but I'm drawing a blank...:smile:

What is the slope of a line perpendicular to x - 3y = 9?

Notes:
Perpendicular lines have slopes that are negative reciprocals of each other.

Example: So, if the original line has a slope of -3/2, the line perpendicular to the original line has a slope of 2/3.

So, if I work that problem out, I get...

-3y = 9 - x
y = 9 - x/-3
y =

That is where I'm locked up...what do I do with the x? It's been a while since I've done this (The last time I turned any homework in in this class was eight days ago. I've been juggling catching this class up and keeping up in Chemistry so...:bugeye: ) so I'm, more than likely, just having a brain fart.:-p
 
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  • #2
y=mx + b

where m is equal to the slopeNow, what is your slope for the equation x - 3y = 9
when you solve for y?
Essentially, what is the coefficient multiplying x?

For example, in y=4x + 2
the slope is 4

Now to get the negative reciprocal, you know how to do...I'm going to be painfully honest with you, you should have known this. If you are juggling catching this class up and keeping up in chemistry, I suggest you go into tutoring to let all the math just really kick in. If you start understanding it, you will have to put in far less effort afterwards. Chemistry, try to do some group studying!

Good luck!
 
  • #3
Tutoring and group studying sounds like a "painfully honest" and simple solution but it isn't. I'm not a public school student, I'm a cyber student. I don't even have books let alone teachers. I had trouble with Trig so my Dad tried to find a tutor several ways. He checked with a college near here (Juniata), my public high school, and my cyber school- nothing. The college didn't get back to us for a while, my high school sent out an email to the math department only to get no replies, and my cyber school suggested the college...when we had already checked. And as for group studying, nothing like that existed at my school and it certainly doesn't in this one. If it did, I doubt as many kids would be failing when the grading system was changed so that anything beneath a 65% is failing when it used to be 70%. As my "mentor" put it, "We aren't teachers, we're 'mentors" because, technically, we aren't teaching you; you're teaching yourself."

And, to explain why I'm working on catching up in Math just in case I seem like a slacker:-p , as I stated already, I had trouble with Trig. I solved that problem by dropping that class and replacing it with my current one. It took me two weeks to do so because my teacher argued with me saying that I could do it even though I clearly could not. That means, I had to catch up...I was behind by 35 assignments two weeks ago. Currently, I'm all caught up.:wink:

Now, onto the actual question.:biggrin:

I know I'm to be solving for y as I began to do above. However, I got to a point where I couldn't figure out what to do. Is this right?

y = 1/3x - 3

So, the slope in that would be 1/3 making my answer...-3?
 
  • #4
AngelShare said:
I know I'm to be solving for y as I began to do above. However, I got to a point where I couldn't figure out what to do. Is this right?
y = 1/3x - 3
So, the slope in that would be 1/3 making my answer...-3?
That's correct :smile:
 

Related to Slope of Perpendicular Line to x - 3y = 9

1. What is the equation of a perpendicular line to x - 3y = 9?

The slope of a perpendicular line is the negative reciprocal of the slope of the given line. In this case, the slope of x - 3y = 9 can be rewritten as y = (1/3)x - 3. The negative reciprocal of 1/3 is -3, so the equation of the perpendicular line would be y = -3x + b, where b is the y-intercept.

2. How do you find the slope of a perpendicular line?

To find the slope of a perpendicular line, you need to take the negative reciprocal of the slope of the given line. This means flipping the fraction and changing the sign. For example, if the given line has a slope of 2/5, the perpendicular line would have a slope of -5/2.

3. Can the slope of a perpendicular line be undefined?

No, the slope of a perpendicular line cannot be undefined. In order for a line to be perpendicular, it must intersect the given line at a 90 degree angle, meaning it must have a defined slope. However, the slope of a perpendicular line can be 0, which would result in a horizontal line.

4. How can you determine if two lines are perpendicular using their equations?

If two lines have slopes that are negative reciprocals of each other, then they are perpendicular. This means that if the slope of one line is m, the slope of the other line would be -1/m. You can use this information to compare the slopes of the given lines and determine if they are perpendicular.

5. Can the slope of a perpendicular line be the same as the slope of the given line?

No, the slope of a perpendicular line cannot be the same as the slope of the given line. If two lines have the same slope, they are parallel and not perpendicular. In order for a line to be perpendicular, it must have a slope that is the negative reciprocal of the slope of the given line.

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