Question 1004934
If the charges per minute for the 2 months
are not the same, then I can assume there is 
a fixed monthly charge also
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The linear equation has the form:
{{{ y = m*x + b }}}
{{{ y }}} is the total charge for a particular month
{{{ m }}} is the [ cost ] / [ min ] which has to be determined
{{{ b }}} is the fixed monthly cost which will be the same
for every month which has to be determined
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With the given data, I can say:
(1) {{{ 1941 = m*52 + b }}}
(2) {{{ 4565 = m*380 + b }}}
( both y's are in cents )
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There are 2 equations and 2 unknowns, so it's solvable
Subtract (1) from (2)
(2) {{{ 4565 = m*380 + b }}}
(1) {{{ -1941 = -m*52 - b }}}
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{{{ 2624 = 328m }}}
{{{ m = 8 }}} ( this is [ cents ] / [ min ] )
This is the rate she is being charged
plug this value back into either of the equations to find {{{ b }}}
(1) {{{ 1941 =8*52 + b }}}
(1) {{{ 1941 = 416 + b }}}
(1) {{{ b = 1525 }}}
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The linear equation is:
{{{ y = 8x + 1525 }}} ( in cents )
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check:
(2) {{{ 4565 = m*380 + b }}}
(2) {{{ 4565 = 8*380 + b }}}
(2) {{{ 4565 = 3040 + b }}}
(2) {{{ b = 1525 }}}
OK
Here is a plot of the equation:
{{{ graph( 400, 400, -50, 500, -600, 6000, 8x + 1525 ) }}}