Question 727411: find the equation of the line that has the points (1/4,-1/3),(-1/4,-3).write the equation in standard form
Found 2 solutions by mananth, Edwin McCravy:
Answer by mananth(16946)   (Show Source):
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
The above solution contains a sign error.
First we use the slope formula:
m = 
where (x1,y1) = ( , ).
and where (x2,y2) = ( ,-3).
m =  =  =  =  =  =  = 
Next we use the point slope formula:
Point-slope formula:
y - y1 = m(x - x1)
where (x1,y1) = (,), m =
y - = (x - )
y +  = (x - )
Multiply through by 3
3y + 1 = 16(x - )
3y + 1 = 16x - 4
-16x + 3y = -5
Multiply through by -1
16x - 3y = 5
-------------------------------------
Here is another way to do it:
Substitute both points in
y = mx + b
Substituting (x,y) = (,).
= m + b
Simplify by multiplying through by LCD = 12
-4 = 3m + 12b
Substituting (x,y) = (,-3).
-3 = m + b
Simplify by multiplying through by LCD = 4
-12 = -m + 4b
So you have the system of equations:
-4 = 3m + 12b
-12 = -m + 4b
Multiply the bottom equation through by 3 to make the m
terms cancel, then add the equations term by term:
-4 = 3m + 12b
-36 = -3m + 12b
---------------
-40 = 24b
 = b
 = b
-4 = 3m + 12b
-12 = -m + 4b
Multiply the bottom equation through by -3 to make the b
terms cancel, then add the equations term by term:
-4 = 3m + 12b
36 = 3m - 12b
---------------
32 = 6m
 = m
= m
So the equation in y-intercept form is
y = x +
y = x - 
3y = 16x - 5
-16x + 3y = -5
16x - 3y = 5
Edwin
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