Question 1055929
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.
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{{{ 8x  - 6y = -2 }}}
{{{ 4x - 3y = -1 }}}
{{{ 3y = 4x + 1 }}}
{{{ y = (4/3)*x + 1/3 }}}
The slope is {{{ m = 4/3 }}} , and any line perpendicular to this one 
will have slope 
{{{ m[1] = -1/m }}}
{{{ m[1] = -1/(4/3) }}}
{{{ m[1] = -3/4 }}}
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Find the y-intercept:
{{{ -6x + 2y = 4 }}}
{{{ -3x + y = 2 }}}
{{{ y = 3x + 2 }}}
{{{ y = 2 }}} is the y-intercept, so now you have the point ( 0,2 )
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Use the general point-slope formula:
{{{ ( y - 2 ) / ( x - 0 ) = -3/4 }}}
Multiply both sides by {{{ 4x }}}
{{{ 4*( y - 2 ) = -3x }}}
{{{ 4y - 8 = -3x }}}
{{{ 4y = -3x + 8 }}}
{{{ y = -(3/4)*x + 2 }}}
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check answer:
Does it go through ( 0,2 ) ?
{{{ 2 = -(3/4)*0 + 2 }}}
{{{ 2 = 2 }}}
OK
Here's a plot of all 3 lines:
( the line with negative slope is the answer )
{{{ graph( 400, 400, -10, 10, -10, 10, (4/3)*x + 1/3, -(3/4)*x + 2, 3x + 2 ) }}}