SOLUTION: 8x-6y=-2 having the same y-intercept as -6x+2y=4. I got y=8/6x+2/6 for the first problem, and y=3x+2 for the second problem. I'm lost as to how do I get the final equation. And

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 8x-6y=-2 having the same y-intercept as -6x+2y=4. I got y=8/6x+2/6 for the first problem, and y=3x+2 for the second problem. I'm lost as to how do I get the final equation. And       Log On


   

Question 1055929: 8x-6y=-2 having the same y-intercept as -6x+2y=4.
I got y=8/6x+2/6 for the first problem, and y=3x+2 for the second problem. I'm lost as to how do I get the final equation. And the final equation has to be perpendicular to 8x-6y=-2, with the same y-intercept as -6x+2y=4
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If that's the whole problem:
" perpendicular to 8x-6y=-2, with the same y-intercept as -6x+2y=4 ",
then you'll have a slope and a point, which is all you need to get
an equation.
----------------------------
+8x++-+6y+=+-2+
+4x+-+3y+=+-1+
+3y+=+4x+%2B+1+
+y+=+%284%2F3%29%2Ax+%2B+1%2F3+
The slope is +m+=+4%2F3+ , and any line perpendicular to this one
will have slope
+m%5B1%5D+=+-1%2Fm+
+m%5B1%5D+=+-1%2F%284%2F3%29+
+m%5B1%5D+=+-3%2F4+
------------------------------
Find the y-intercept:
+-6x+%2B+2y+=+4+
+-3x+%2B+y+=+2+
+y+=+3x+%2B+2+
+y+=+2+ is the y-intercept, so now you have the point ( 0,2 )
-------------------------------
Use the general point-slope formula:
+%28+y+-+2+%29+%2F+%28+x+-+0+%29+=+-3%2F4+
Multiply both sides by +4x+
+4%2A%28+y+-+2+%29+=+-3x+
+4y+-+8+=+-3x+
+4y+=+-3x+%2B+8+
+y+=+-%283%2F4%29%2Ax+%2B+2+
---------------------------
check answer:
Does it go through ( 0,2 ) ?
+2+=+-%283%2F4%29%2A0+%2B+2+
+2+=+2+
OK
Here's a plot of all 3 lines:
( the line with negative slope is the answer )