Question 117882
Basically, {{{C = f(x)}}} and {{{f(x)}}} is linear (straight line)
The general equation for a straight line is {{{y = mx + b}}}
where {{{m}}} is the slope and {{{b}}} is the y-intercept. How
can I modify this general equation for use in this problem?
{{{C}}} will take the place of {{{y}}}. I will have to find out
values for {{{m}}} and {{{b}}} based on data given.
{{{C = mx + b}}}
{{{10000 = 100m + b}}}
{{{22000 = 300m + b}}}
This is 2 equation and 2 unknowns, so I can solve it
Multiply the 1st by {{{3}}} and subtract the 2nd from the 1st
{{{30000 = 300m + 3b}}}
{{{22000 = 300m + b}}}
{{{8000 = 2b}}}
{{{b = 4000}}}
Substitute this into the 1st
{{{10000 = 100m + 4000}}}
{{{100m = 6000}}}
{{{m = 60}}}
Plugging {{{m}}} and {{{b}}} back into the general equation,
{{{C = 60x + 4000}}} answer
check answer
Does this equation work with given data?
{{{C = 60x + 4000}}}
{{{10000 = 60*100 + 4000}}}
{{{10000 = 6000 + 4000}}}
{{{10000 = 10000}}}
OK
{{{22000 = 60*300 + 4000}}}
{{{22000 = 18000 + 4000}}}
{{{22000 = 22000}}}
OK