Question 945566
Change to slope-intercept form:
{{{ 4x + 3y = 4 }}}
{{{ 3y = -4x + 4 }}}
{{{ y = -(4/3)*x + 4/3 }}}
The slope is {{{ m = -4/3 }}}
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Any line perpendicular to this line
has slope {{{ m[1] = -1/m }}}
{{{ m[1] = -1/(-4/3) }}}
{{{ m[1] = 3/4 }}}
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given: ( 2,2 )
Use the general point-slope formula
{{{ ( y - 2 ) / ( x - 2 ) = 3/4 }}}
{{{ y - 2 = ( 3/4 )*( x-2 ) }}}
{{{ y = (3/4)*x - 3/2 + 2 }}}
{{{ y = ( 3/4 )*x + 1/2 }}}
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Here are the plots:
{{{ graph( 400, 400, -6, 6, -6, 6, -(4/3)*x + 4/3, ( 3/4 )*x + 1/2 ) }}}