Question 69565
This is just like writing the equation of a line that passes through two given point. You can treat the cost variable, C as the dependent variable abd the number of items variable, x as the independent variable.
THe equation can be in the slope-intercept form: 
{{{C = mx+b}}}
Let's first find the slope using the two given points: (100, 10,000) and (300, 22,000)
{{{m = (22000-10000)/(300-100)}}} Simplifying this we get:
{{{m = 12000/200}}}
{{{m = 60}}}
So, we can write:
{{{C = 60x + b}}} So now we need to find the value of b.  We can do this by substituting one set of the given values for x and C (x, C) = (100, 10,000) and solve for b.
{{{10000 = 60(100) + b}}} Simplifying, we get:
{{{10000 = 6000 + b}}} Subtracting 6000 from both sides, we get:
{{{4000 = b}}} Now we can write the complete equation relating the cost, C and the number of items produced, x.
{{{C = 60x + 4000}}} This is the required linear equation!