SOLUTION: find the equation of a line that passes through the points(1/4,-1/3)(-1/4,-3)

Algebra ->  Linear-equations -> SOLUTION: find the equation of a line that passes through the points(1/4,-1/3)(-1/4,-3)      Log On


   

Question 726844: find the equation of a line that passes through the points(1/4,-1/3)(-1/4,-3)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
So I don't have to use fractions,
I'll say +a+=+1%2F12+, so
+1%2F4+=+3a+
+-1%2F4+=+-3a+
+-1%2F3+=+-4a+
-----------------
( 3a, -4a ), ( -3a, -3 )
Use point slope formula

+%28+y++%2B+3+%29+%2F+%28+x++%2B+3a+%29+=+%28+-4a+%2B+3+%29+%2F+%28+3a++%2B+3a+%29+
+%28+y++%2B+3+%29+%2F+%28+x++%2B+3a+%29+=+%28+-4a+%2B+3+%29+%2F+6a+
Multiply both sides by +6a%2A%28+x+%2B+3a+%29+
+6a%2A%28+y+%2B+3+%29+=+%28+-4a+%2B+3+%29%2A%28+x+%2B+3a+%29+
+6a%2Ay+%2B+18a+=+-4a%2Ax+%2B+3x+-12%2Aa%5E2+%2B+9a+
+6a%2Ay+=+%28+3+-+4a+%29%2Ax+-+12%2Aa%5E2+-+9a+
Substitute +a+=+1%2F12+
+%281%2F2%29%2Ay+=+%28+3+-+1%2F3+%29%2Ax+-+12%2A%281%2F144%29+-+9%2A%281%2F12%29+
+%281%2F2%29%2Ay+=+%28+8%2F3+%29%2Ax+-+1%2F12+-+9%2F12+
Multiply both sides by +12+
+6y+=+32x+-+10+
+y+=+%28+16%2F3+%29%2Ax+-+5%2F3+
check:
does it go through ( 1/4, -1/3 ) ?
+-1%2F3+=+%28+16%2F3+%29%2A%281%2F4%29+-+5%2F3+
+-1%2F3+=+4%2F3+-+5%2F3+
+-1%2F3+=+-1%2F3+
OK -you can check the other point