Question 880335
Find the slope of the given line
{{{ -5x + 6y = -2 }}}
{{{ 6y = 5x - 2 }}}
{{{ y = (5/6)*x - 1/3 }}}
This is in the form {{{ y = m*x + b }}}
where {{{ m }}} = slope, so
{{{ m = 5/6 }}}
Any line parallel to this line will
have the same slope
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given the point (4,-2)
Use the general point-slope formula
{{{ ( y -(-2) ) / ( x - 4 ) = 5/6 }}}
{{{ y + 2 = (5/6)*( x - 4 ) }}}
{{{ 6*( y + 2 ) = 5*( x - 4 ) }}}
{{{ 6y + 12 = 5x - 20 }}}
{{{ 5x - 6y = 32 }}} answer
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check:
does it go through (4,-2) ?
{{{ 5x - 6y = 32 }}}
{{{ 5*4 - 6*(-2) = 32 }}}
{{{ 20 + 12 = 32 }}}
{{{ 32 = 32 }}}
OK