Question 1050683
Find the point of intersection
{{{ y = 2x - 1 }}}
{{{ y = -(1/2)*x + 4 }}}
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By substitution:
{{{ 2x - 1 = -(1/2)*x + 4 }}}
Multiply both sides by {{{ 2 }}}
{{{ 4x - 2 = -x + 8 }}}
{{{ 5x = 10 }}}
{{{ x = 2 }}}
and
{{{ y = 2x - 1 }}}
{{{ y = 2*2 - 1 }}}
{{{ y = 3 }}}
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The intersection is at ( 2,3 )
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Now find the y-intercepts
by setting {{{ x = 0 }}}
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{{{ y = 2x - 1 }}}
{{{ y = 2*0 - 1 }}}
{{{ y = -1 }}}
( 0, -1 ) 
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{{{ y = -(1/2)*x + 4 }}}
{{{ y = -(1/2)*0 + 4 }}}
{{{ y = 4 }}}
( 0, 4 }
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The distance between the 2 y-intercepts is:
{{{ abs( 4 -(-1) ) }}}
{{{ abs( 5 ) = 5 }}}
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The height of the triangle formed is
the x-value of the intersection ( 2,3 )
which is {{{ 2 }}}
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{{{ A = (1/2)*5*2 }}}
{{{ A = 5 }}} 
The area is 5 square units
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Here's the plot of the lines:
{{{ graph( 400, 400, -10, 10, -10, 10, 2x - 1, -(1/2)*x + 4 ) }}}