Question 1079202
The given line is:
{{{ 2x - y  + 3 = 0 }}}
{{{ y = 2x + 3 }}}
The slope is  {{{ m[1] = 2 }}}
Any line perpendicular to this line
will have slope {{{ m[2] = -1/2 }}}
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The lines intersect at ( x1, 0 )
For the given line:
{{{ 0 = 2*x[1] + 3 }}}
{{{ 2x[1] = -3 }}}
{{{ x[1] = -3/2 }}}
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The unknown line is:
{{{ y = (-1/2)*x + b }}}
Plug in the point ( -3/2, 0 )
{{{ 0 = (-1/2)*(-3/2) + b }}}
{{{ ( 3/4 ) + b = 0 }}}
{{{ b = -3/4 }}}
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The unknown line is:
{{{ y = (-1/2)*x - 3/4 }}}
{{{ 4y = -2x - 3 }}}
{{{ 2x + 4y + 3 = 0 }}}
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Here's the plot of the 2 lines:
{{{ graph( 400, 400, -6, 6, -6, 6, 2x + 3, (-1/2)*x - 3/4 ) }}}