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Question 785566: Good morning,
I'm a student of San Francisco State University and I have a series of questions on the website WileyPLUS. I'm not really a fan of it because its all computer and I dont know if I enter my answer wrong or if its my answer that is totally wrong.
Here is the example:
Write an equation for the line through (-3, 2) and (6, 1)
Give an exact coefficients in fraction form.
y = f(x) = [a computer table that allows us to put an answer]
So, I came up with the slope (m) that is 1-2/6-(-3) = -1/9
so, now, I have y = -1/9x + b
I change into 2 = -1/9 (-3) + b
18/9 = -1/9 (-27/9) + b
-b = -27-162/-81
-b = -199/-81
-b = 199/81
b = -199/81
So I change everything into : 2 = -1/9 (-3) + -199/81
I dont know if I am wrong or if the computer (website) is not expecting an answer this form.
Maybe I should not use x and y as they are different at every point.
But I tried everything already... and every time, I am wrong, the website is giving me a different exercise numbers...
Please help me! Is my Math correct?
thank you!!!!
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Write an equation for the line through (-3, 2) and (6, 1)
Give an exact coefficients in fraction form.
y = f(x) = [a computer table that allows us to put an answer]
So, I came up with the slope (m) that is 1-2/6-(-3) = -1/9
so, now, I have y = -1/9x + b
I change into 2 = -1/9 (-3) + b
-----------
2 = 1/3 + b
b = 5/3
**********************
I don't know what you're up to there.
--------------------------
y = -x/9 + 5/3
=================================
18/9 = -1/9 (-27/9) + b
-b = -27-162/-81
-b = -199/-81
-b = 199/81
b = -199/81
So I change everything into : 2 = -1/9 (-3) + -199/81
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! MINOR NOTE:
If you cannot write the calculation on two lines, it should be
m=(1-2)/(6-(-3)) = -1/9
I can guess what you meant, and  is correct.
However, most computers and calculators will interpret what you enter literally.
Those machines are sticklers about order of operations, and if you do not enter the parentheses, they will not guess at what you meant, like I did.
They will just calculate
m = 1-2/6-(-3) = 
You came up with the slope (m) that is  and that reassured me that I was guessing right.
WHAT YOU DID RIGHT:
The slope is indeed  .
Your idea for finding the equation was not bad.
Substituting , and the x- and y-coordinates of (-3,2) into  would allow you to find the y-intercept (b).
You just unnecessarily complicated the calculations
(partly by not simplifying fractions when possible),
and that led to cumersone calculations that led you to a silly mistake.
It happens to the best of us.
Here is how it should go:
 (product of two negative numbers is positive, just multiply the absolute values, ignoring the minus signs)
 (multiplying fractions)
 (simplifying the fraction makes the work easier down the line)
 (now I may be forced to find a common denominator, I did not need to do that before)
You should write the equation in slope-intercept form (y=mx+b) as
y=(-1/9)x+5/3 and the computer should understand 
If it translates it and shows you that, you lknow you got it right.
If you typed y=-1/9x+5/3, the computer may interpret 
and I would toss a coin to figure out if you meant that or .
An optional form of the solution would be
y=-x/9+5/3 which can be rendered as 
I would not know if that is one on the accepted answers, because computer tests are tricky.
YOUR COMPLICATIONS AND MISTAKE:
18/9 = -1/9 (-27/9) + b is true, but unnecessarily complicated
-b = -1/9 (-27/9)-18/9 is true, but complicated further by insisting on having b on the left side.
By then your head was spinning and you were bound to make a mistake.
Then, multiplying -1/9 (-27/9) = 1/9 (27/9) = 1*27/(9*9) = 27/81,
without noticing that the fraction 27/81 = 1/3 can be simplified
would have taken you to
-b = 27/81-18/9 --> -b = 27/81 -162/81 --> -b = (27-162)/81
Unfortunately, you got the wrong sign on the product, and ended up with
-b = (-27-162)/(-81) which you probably wrote as  on paper, but type here as
-b = -27-162/-81 (I know what you mean, but a computer would not know).
That yielded -b = (-199)/(-81), -b = 199/81, and b = -199/81, which is wrong.
IN SUM:
Simplify fractions whenever possible.
Watch out for minus signs and parenteses.
If the numbers/fractions in a class problem seem to get to complicated, you probably made a mistake somewher, and maybe there is an easier route to the solution.
BONUS INFORMATION:
If you have the slope and one point you can write the equation in point-slope form by filling the blanks in
y - ___ = m (x - ___ ) withe the x- and y-coordinates of your point.
If you chose point (-3,2), you would write
Form there, you get
 (simplifying the fraction)
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