Question 1010453
This is a straight line relation and the slope is
[ dues ] / [ month ]
Let {{{ C }}} = total cost including initiation plus dues
Let {{{ n }}} = number of months the dues are paid
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Plot {{{ C }}} on the vertical axis and
plot {{{ n }}} on the horizontal axis
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You are given the points:
( 7, 335 )
( 18, 830 )
Use the general point-slope formula
{{{ ( C - 335 ) / ( n - 7 ) = ( 830 - 335 ) / ( 18 - 7 ) }}}
{{{ ( C - 335 ) / ( n - 7 ) = 495 / 11 }}}
{{{ 11*( C - 335 ) = 495*( n - 7 ) }}}
{{{ 11C - 3685 = 495n - 3465 }}}
{{{ 11C = 495n + 220 }}}
{{{ C = 45n + 20 }}}
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check answer:
( 7, 335 )
{{{ C = 45n + 20 }}}
{{{ 335 = 45*7 + 20 }}}
{{{ 335 = 315 + 20 }}}
{{{ 335 = 335 }}}
and
( 18, 830 )
{{{ C = 45n + 20 }}}
{{{ 830 = 45*18 + 20 }}}
{{{ 830 = 810 + 20 }}}
{{{ 830 = 830 }}}
OK
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The monthly dues is the slope of the line, so
dues = $45
The initiation fee is the intercept on the vertical
axis, found by setting {{{ n = 0 }}}
{{{ C = 45*0 + 20 }}}
{{{ C = 20 }}}, so
initiation = $20
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Here's the plot:
{{{ graph( 400, 400, -2, 20, -100, 1000, 45x + 20 ) }}}
Here's a close-up of the C-intercept:
{{{ graph( 400, 400, -1, 2, -3, 30, 45x + 20 ) }}}