Question 1065150
{{{ y = -(4/3)*x - 9 }}}
{{{ m = -4/3 }}}
The slope of the perpendicular line is:
{{{ m[1] = -1/m }}}
{{{ m[1] = -1/(-4/3) }}}
{{{ m[1] = 3/4 }}}
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The general form of the required line is:
{{{ y = m[1]*x + b }}}
{{{ y = (3/4)*x + b }}}
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The x-intercept of {{{ 3x - 5y = -6 }}}
is where {{{ y = 0 }}}, so
{{{ 3x - 5*0  = -6 }}}
{{{ 3x = -6 }}}
{{{ x = -2 }}}
So, you are given the point ( -2, 0 )
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{{{ y = (3/4)*x + b }}}
{{{ 0 = (3/4)*(-2) + b }}}
{{{ 0 = -3/2 + b }}}
{{{ b = 3/2 }}}
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The equation of the line is:
{{{ y = (3/4)*x + 3/2 }}}
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check:
Does it go through ( -2,0 ) ?
{{{ 0 = (3/4)*(-2) + 3/2 }}}
{{{ 0 = -3/2 + 3/2 }}}
{{{ 0 = 0 }}}
OK