Question

Which equation represents the line passing through the points (3,2) and (-9,6)

Answer 1

Possible answers:
A. x-3y=9
B. x+3y=9
C. 3x-y=-9
D. 3x+y=9

Answer 2

@mathmale

Answer 3

Hola, Daniel! Que va? Como estas?

Answer 4

Bien y tu?

Answer 5

I would take those two points, find the slope (m), and then write the equation of the line in point-slope form. Bien! Gracias.

Answer 6

m=0.33333

Answer 7

Bet you already know the formula for slope:\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 8

sorry -0.33333

Answer 9

and also that you know the point-slope form:\[y-y _{0}=m(x-x _{0})\]

Answer 10

Daniel: Think: As you go from (-9,6) to (3,2), it does seem that y is decreasing as x increases. Therefore, your negative slope makes sense!

Answer 11

yes

Answer 12

You may use either -0.333333 or -1/3 for the slope, m. I'd use m=-1/3 myself.

Please choose either point (it doesn't matter which one). Substitute the coordinates of that chosen point into the point-slope form of the eq'n of a straight line, along with your value of m. What do you get?

Answer 13

Once you have this result, you need only re-arrange the terms so that x comes first and y second in the "equation of a line in 'standard form' ", with a constant on the right.

Answer 14

slope is -1/3
select either point and substitute the points x and y values into the point slope form equation just like @mathmale said
i would choose (3,2) as it is smaller
y-2=-1/3(x-3)
now just change it into slope intercept form

Answer 15

y=-0.3x+2.9

Answer 16

Daniel, please multiply both sides of your result by 10 to eliminate the decimal fractions.
Then rearrange your equation so that you have 3x on the left, followed by 1y, followed by an equal sign and a constant.

Answer 17

nvr mind sorry i forgot to look at the answer choices
change it to standard form and use -1/3 for slope

Answer 18

10y=-3x+29

Answer 19

10y+3x=29

Answer 20

or 3x + 10y = 29. Looks very nice. Does this match any of the four possible answers?

Answer 21

nop

Answer 22

Darn. I'm going to go back and review what you're done in the hope of being able to point out what went wrong, if anything. In the meantime, why not look at the next homework problem you need to do?

Answer 23

OK

Answer 24

just check on the graphing calculator
https://www.desmos.com/calculator

Answer 25

y-2=-1/3(x-3)
y-2=-1/3x+1
y=-1/3x+3
1/3x+y=3
x+3y=9

Answer 26

the answer is b

Answer 27

it is b
i checked on the graph website

Answer 28

you didn't have to use point slope form

Answer 29

Confirming that your slope, m, is correct: m = -1/3.
Next time, share what you've done towards finding the equation of the line.

I would choose the point (3,2). Then x=3 and y=2. Substituting these, and m = -1/3, into the point-slope formula results in

\[y-2=\frac{ -1 }{ 3 }(x-3)\]Daniel: Would you plese simplify this? the first thing I'd do would be to multiply everything in this equation by 3, to remove the fractions.

Answer 30

i already simplified it @danielbarriosr1

Answer 31

you could have just used y = mx + b form

Answer 32

There are, of course, various ways in which to do this problem; I tend to use the point-slope form because it's so easy and straightforward. It's also easy to change from one form to another that way.

Daniel? How are you doing in terms of simplifying this equation?

Answer 33

Im on it

Answer 34

Several of you are trying to help at the same time. If you have an alternative approach, and see nothing wrong with the one I'm using, I ask that you please wait until Daniel is finished BEFORE proposing an alternative approach. Also, remember, the goal is for Daniel to learn how to do these problems himself, not for you to provide answers. Thanks.

Answer 35

y=-1/3x+3

Answer 36

Daniel, here's what I was suggesting earlier: Please multiply the following equation (that is, each term of the following equation) by 3 to eliminate the fraction:\[3[y-2=\frac{ -1 }{ 3 }(x-3)\]

Answer 37

The result is 36 - 6 = -(x-3). Are you comfortable with this, Daniel?

Answer 38

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

Answer 39

where does the 36 came from?

Answer 40

yeah?

Answer 41

Typo. Your version is correct. Proceed, please.

Answer 42

3y-6=-x+3

Answer 43

3y=-x+9

Answer 44

Great. Please move that x to the left side of your equation, and then youi'll be done.

Answer 45

y+1/3x=3

Answer 46

You had 3y=-x+9.

I'd suggest you'd find it easier if you'd please just add x to both sides. NO division.
Why: Because there are NO fractions in any of the four possible answers.

Answer 47

oh

Answer 48

So that results in x+3y=?

Answer 49

Is your result the same as any of the four possible answers?

Answer 50

x+3y=9

Answer 51

Yes... B.

Answer 52

Thank you @mathmale

Answer 53

Cool! Congrats!!

@acxbox22 claims that he has a faster approach. Daniel, it's entirely up to you to choose whether you want him/her to present that approach or to let you move on to the next homework problem. De nada!

Answer 54

and thank you @acxbox22 of course

Answer 55

it is allright as i already showed him my approach 15 posts earlier

Answer 56

But I prefer @mathmale 's explanations

Answer 57

no problem

Answer 58

Thank you, Dan. I'd like to point out that acxbox22 did obtain the correct result with less work, but essentially he followed the same procedure as you and I did. I just prefer to explain problem solutions verbally instead of with just equations.

Suggest we move on immediately to your next homework problem, if there is one.

@acxbox22: Sincere thanks for your contributions here.

Answer 59

Ok...

Answer 60

Which equation represents the line passing through the point (4,-16) and is perpendicular to the line...

Answer 61

perpendicular to the line y=-2/3x+8

Answer 62

possible answers:
A. y=2/3x-22
B. y=-2/3x-22
C. y=-3/2x-22
D. y =3/2x-22

Answer 63

do you know perpendicular lines?

Answer 64

I know I can eliminate B and C because that slope would make them parallel

Answer 65

Those are the lines that intersect at one point

Answer 66

I think is D.

Answer 67

you can eliminate B but not C since it does not have the same slope in fact you can find out the answer without much work

Answer 68

But C is negative

Answer 69

perpendicular means opposite reciprocal
what is the opposite reciprocal of -2/3?
if you find that out then you will know the answer since each answer choice's slopes are different

Answer 70

3/2

Answer 71

D right?

Answer 72

exactly..
d is your answer

Answer 73

Thanks

Answer 74

np

Answer 75

it is b

Answer 76

no b would make it parallel not perpendicular

Answer 77

It is supose to be perpendicular no parllel

Answer 78

oh