Question 145848
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Stanbon's solution is incorrect!
Here is the correct solution!

Solution by Edwin:
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Write an equation in standard form with integar coefficients for the line with slope {{{3/17}}} going through point (-5,-5).
       
The equation of the line is __x _ __y=___
(Use integer coeffients for the equation. Make sure the coefficient of x is positve and the greatest common divisor of the coefficient is 1)
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y-y<sub>1</sub> = m(x-x<sub>1</sub>)

{{{y-(-5) = (3/17)(x-(-5))}}}

{{{y+5=(3/17)(x+5)}}}  

<font color = "red">---(you missed a sign in this step unless
you typed -5 and meant 5 in the original 
problem. Now you should not try to keep 
fractions, because they slow down your 
work.  A good rule with few exceptions 
is: whenever you encounter fractions in
an equation, clear of fractions. 
So...)---</font>

Multiply both sides by {{{17}}}, written as
{{{17}}} on the left and as {{{17/1}}} on the
right:

{{{17(y+5)=(17/1)(3/17)(x+5)}}}

Distribute on the left and cancel {{{17}}}'s on
the right:

{{{17y+85=(cross(17)/1)(3/cross(17))(x+5)}}}

{{{17y+85=3(x+5)}}}

Distribute on the right:

{{{17y+85=3x+15}}}

You can get the final answer from there 
by either transposing or adding or 
subtracting the same thing to or from 
both sides. Your final answer after 
several steps will be:

{{{3x-17y=70}}}

Edwin
PS
Your work came out all garbled as you can see
below. To see how I typed in the above, right
click then left click on "View Source".

But you don't have to do all that to make a
fraction.  You can make {{{3/17}}} this way: 

                        (3/17)

You don't have to put the numerator above and
the denominator below.  But you have to use
a lot of parentheses to keep the problem from
being misinterpreted.

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MY WORK:  y-y  =m(x-x  )
             1        1
          y-5=3
              _  (x-5)
              17
         y=3
           _ x-10
           17  _
               17
        -__3
          17x+y=-__10
                   17