Question 1049957
(A)
{{{ 3y - 4x = 8 }}}
{{{ 3y = 4x + 8 }}}
{{{ y = (4/3)*x + 8/3 }}}
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The slope of the line through
( 4,4 ) and ( k,8 ) is:
{{{ m = ( 8 - 4 ) / ( k - 4 ) }}}
{{{ m = 4 / ( k - 4 ) }}}
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A line parallel to the given line
will have the same slope
{{{ 4 / ( k-4 ) = 4/3 }}}
{{{ k - 4 = 3 }}}
{{{ k = 7 }}}
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(B)
{{{ 4y + 5x = 3 }}}
{{{ 4y = -5x + 3 }}}
{{{ y = -(5/4)*x + 3/4 }}}
{{{ m[1] = -(5/4) }}}
Any line perpendicular to this line
will have slope:
{{{ m[2] = -1/m[1] }}}
{{{ m[2] = -1/(-(5/4)) }}}
{{{ m[2] = 4/5 }}}
{{{ 4/( k-4 ) = 4/5 }}}
{{{ k - 4 = 5 }}}
{{{ k = 9 }}}