Question 1037043
If you are given a line with slope  = {{{ m[1] }}},
then ANY line perpendicular to the given line
will have slope  = {{{ m[2] = -1/m[1] }}}
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You are given:
{{{ y - 3 = -(1/5)*x + 2 }}} ( is this it? Is there a typo? )
{{{ y = -(1/5)*x + 5 }}}
The slope is: {{{ m[1] = -(1/5) }}}
Any line perpendicular to this line has slope:
{{{ m[2] = -1 / ( -(1/5) ) }}}
{{{ m[2] = 5 }}}
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The line you are looking for passes through (-2,7 )
Use the general point-slope formula:
{{{ ( y - 7 ) / ( x - (-2) ) = 5 }}}
{{{ y - 7 = 5*( x + 2 ) }}}
{{{ y - 7 = 5x + 10 }}}
{{{ y = 5x + 17 }}} answer
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check:
does the line go through (-2,7) ?
{{{ y = 5x + 17 }}}
{{{ 7 = 5*(-2) + 17 }}}
{{{ 7 = -10 + 17 }}}
{{{ 7 = 7 }}} 
OK
Here is a plot of the 2 lines:
{{{ graph( 500, 500, -26, 26, -24, 24, -(1/5)*x + 5, 5x + 17 ) }}}