Question 610080
First, choose the form of the equation.
{{{ y = m*x + b }}} is the slope-intercept form
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The line goes through (2,1), so I can say
(1) {{{ 1 = m*2 + b }}}
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The line goes through (-3,5), so I can say
(2) {{{ 5 = m*(-3) + b }}}
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(1) {{{ 2m + b = 1 }}}
(2) {{{ -3m + b = 5 }}}
Subtract (2) from (1)
(1) {{{ 2m + b = 1 }}}
(2) {{{ 3m - b = -5 }}}
{{{ 5m = -4 }}}
{{{ m = -4/5 }}}
So far I have 
{{{ y = (-4/5)*x + b }}}
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Now plug (x,y) in from either of the 2 points
(2,1)
{{{ 1 = (-4/5)*2 + b }}}
{{{ 1 = -8/5 + b }}}
{{{ b = 5/5 + 8/5 }}}
{{{ b = 13/5 }}}
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The equation of the line is:
{{{ y = (-4/5)*x + 13/5 }}}
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check:
(2,1)
{{{ 1 = (-4/5)*2 + 13/5 }}}
{{{ 1 = -8/5 + 13/5 }}}
{{{ 1 = 5/5 }}}
{{{ 1=1 }}}
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(-3,5)
{{{ 5 = (-4/5)*(-3) + 13/5 }}}
{{{ 5 = 12/5 + 13/5 }}}
{{{ 25 = 12 + 13 }}}
{{{ 25 = 25 }}}
OK