Question

Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, −1).

y = one thirdx − 3

y = one thirdx + 17

y = −3x − 3

y = −3x + 17


Someone please help, I have no clue what I am doing.

Answer 1

A perpendicular line has a negative reciprocal for a slope.

Answer 2

OK, I learned this, lol I just don't understand how to get the answer. The way everyone is explaining it, I just don't get it.

Answer 3

3x+y=7, can you solve for y?

Answer 4

Come on, subtract 3x from both sides, what do you get?

Answer 5

Lol I am just viewing this, my baby cousin needed help. Ok let me work this out.

Answer 6

X + Y = 4?

Answer 7

Ok, I am positive I messed that whole thing up.

Answer 8

Are you familiar with the point-slope formula?
http://www.purplemath.com/modules/strtlneq2.htm

Answer 9

Yes, I am, I am learning it in virtual school now. I just don't get it.

Answer 10

I will take a look at that link

Answer 11

You pick a point and substitute those values for \(x_1\) and \(y_1\). You should still have both and x and a y in your equation.

Answer 12

Which numbers? I don't understand.

Answer 13

Line: 3x + y = 7
Point: (6, −1)
Point-Slope formula: \(y – y_1 = m(x – x_1)\)

Answer 14

Because there is already an equation up there, and the coordinates, at this point I have no idea what to do with anything. I am so sorry.

Answer 15

First, find the slope of the perpendicular line.
What is the slope of the given line?

Answer 16

To find the slope, solve for y.
y=mx+b

Answer 17

I do not know the numbers I am substituting, sorry if I was unclear.

Answer 18

OK. The point (6,-1) are the numbers you will be substituting for \((x_1,y_1)\).

Answer 19

\(x_1=6, y_1=-1\)

Answer 20

what would 'm' be?

Answer 21

m is the slope so it will be the negative reciprocal of the original slope.

Answer 22

I have no clue what that number is. At all, I could most likely figure out the equation if I knew it. But I am having a hard time.

Answer 23

Believe it or not, I am actually trying lol, I know I am bad at this.

Answer 24

Start with the given equation: \(3x + y = 7\) and solve for y.

Answer 25

I know you are trying. I'm here to help.

Answer 26

Ok, would I take three to each sides and subtract?

Answer 27

Subtract 3x from each side, yes.

Answer 28

And you are not bad at this, you just haven't learned it yet. Give yourself time.

Answer 29

So would that be Y + -3 =7 or would it be x + y = 4?

Answer 30

\(3x + y = 7\)
\(-3x~~~=-3x\)
--------------
\(y=-3x+7\)
Does that make sense?

Answer 31

Yes, that makes much more sense.
Ok, now I think I should divide now, but I don't know by what.

Answer 32

If y had a coefficient, you would divide. Since it doesn't, you don't need to divide.
Do you know what the slope of this line is?

Answer 33

No, I can't say that I do.

Answer 34

y=mx+b
m=slope
Does that help?

Answer 35

I know m= slope, but I don't know what I am suppose to do now, I don't know where to carry the problem off to.

Answer 36

Going back to the point-slope formula, substitute the negative reciprocal for m in that formula.

Answer 37

I have no clue what that means lol.

Answer 38

The reciprocal means to flip the fraction. Remember that \(3=\frac{3}{1}\)

Answer 39

So three over 1?
Can you show me what I have to do next?

Answer 40

The reciprocal of \(3 = \frac{1}{3}\).
The negative reciprocal of \(3 = -\frac{1}{3}\)

Answer 41

I am still stuck.

Answer 42

In summary:
"Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, −1)."
1. Solve the given line for y.
2. Identify the slope of the given line.
3. Use the point-slope formula to determine the equation of the perpendicular line.
4. Substitute the x and y values from the given point into the point-slope formula.
5. Substitute the negative reciprocal for m in the point-slope formula.
6. Solve for y if requested.

Answer 43

Does this help at all? Which step do you find confusing?

Answer 44

Four, five, and six.

Answer 45

I have to have this test turned in by eleven. But I do not want to make a bad grade on it :/ even though I am bad at math, I manage to make good grades, due to the fact that try extra hard for them.

Answer 46

Write the equation of the line that is perpendicular to the line \(3x + y = 7\) and passes through the point (6, −1).
1. \(y=-3x+7\)
2. \(m=-3\)
3. \(y – y_1 = m(x – x_1)\)
4. Using the point (6,-1). \(y – -1 = m(x – 6)\)
Is this what you have?

Answer 47

I don't believe anyone is "bad at math". If you put in the effort (which you are clearly doing) and find the best explanations for you, you will learn what you need to learn.

Answer 48

Don't be afraid to use many different sources to figure things out. And feel free to play around. Math is all about pattern recognition.

Answer 49

Did you have anything close to what I wrote?

Answer 50

yes I got that, but I don't think that is a choice D:

Answer 51

There are still more steps. In the original equation m=-3, in this equation, the slope should be the negative reciprocal. \(-3 \implies \frac{1}{3}\). Plug that value in for m in this equation.

Answer 52

So, y-1= -3 ( x-6)

Answer 53

And I need to solve?

Answer 54

Your slope is the original slope. The slope for the perpendicular line needs to be the negative reciprocal.

Answer 55

What is the negative reciprocal?

Answer 56

negative means to negate the number. The negation of 4 is -4; the negation of -5 is 5. Negating a number is the same as multiplying it by -1.

Answer 57

The reciprocal means to flip the fraction. Remember that a whole number can be represented by the whole number over 1. For example \(4 = \frac{4}{1}\).

Answer 58

Does that make sense?

Answer 59

So "m" would be Negative 4/1

Answer 60

Your original slope is -3. So, multiply by -1 then flip the fraction.

Answer 61

3/1?

Answer 62

Now, flip the fraction.

Answer 63

1/3?

Answer 64

So 1/3 is 'M"?

Answer 65

Yes.

Answer 66

\(y–−1=\frac{1}{3}(x–6)\)
Now solve the equation.

Answer 67

Solve for y is what I meant.

Answer 68

Y- (-1) right?

Answer 69

If you mean \(y--1=y+1\) then yes. That is the first step to solving this equation.

Answer 70

\(y+1=\frac{1}{3}(x–6)\)

Answer 71

What's next?

Answer 72

I am asking if the one is a negative, I have no clue. I want to say you move some numbers around.

Answer 73

Yes, y--1 = y-(-1).

Answer 74

Can you explain to me how to solve this?

Answer 75

Sure.
You are familiar with the double negative making a positive?
That is how y-(-1) = y+1.

Answer 76

The next step would be to distribute the \(\frac{1}{3}\).

Answer 77

What would that look like?

Answer 78

Number wise.

Answer 79

\(y+1=\frac{1}{3}(x–6)\)
To distribute the \(\frac{1}{3}\) you need to multiply it by each of the terms inside the parenthesis.
\(\frac{1}{3} \times x\) and \(\frac{1}{3}\times -6\)

Answer 80

OK, let me try this, I will show you what I come out with.

Answer 81

I would like to invite you to a whiteboard website. It might be easier to explain this.

Answer 82

I can't do those things due to my limited gigabytes

Answer 83

We can continue to work here. No problem.

Answer 84

Ok So I came out with;
y +1 = 1/3x -2

Answer 85

Yes. One more step to finish.

Answer 86

Ok, I assume it is to do something to the 1?

Answer 87

You assume correctly.

Answer 88

If I disappear for a bit it is because I am babysitting, and my little cousin is sick, so I am going to be up and down.

So would we subtract.. orr?

Answer 89

No problem.
Yes, subtract 1 from both sides.

Answer 90

So subtract one from itself and two?

Answer 91

and the -2, yes.

Answer 92

Ok let me try this.

Answer 93

Effectively moving the 1 to the other side of the equation and combining it with the -2.

Answer 94

Y= 1/3 x - 3 or Y= 1/3x + 3?

Answer 95

\(y=\frac{1}{3}x-3\)

Answer 96

So Y= 1/3x -3? :)

Answer 97

yes, that is the correct answer.

Answer 98

The answer is A? :D