Question

an entrepreneur creating a new game app pays $1,200 monthly for office space and $4,800 to each developer employed. a linear equation modeling these costs per month is $f(x) = 4,800x + 1,200$, where the independent variable is represented by the number of developers, and the dependent variable is represented by the total cost for a given month. describe the solution set.\
\
\\(\\{(0,1200),(1,6000),(2,10800),(3,15600)...\\}\\)\
\\(\\{(1200,0),(6000,1),(10800,2),(15600,3)...\\}\\)\
\\(\\{(1,1200),(2,6000),(3,10800),(4,15600)...\\}\\)\
\\(\\{(1200,1),(6000,2),(10800,3),(15600,4)...\\}\\)

Explanation:

Step1: Define variable meaning

Independent variable $x$ = number of developers (non-negative integers: 0,1,2,3...), dependent variable $f(x)$ = total monthly cost.

Step2: Calculate cost for $x=0$

Substitute $x=0$ into $f(x)=4800x+1200$:
$f(0)=4800(0)+1200=1200$
Gives the pair $(0, 1200)$

Step3: Calculate cost for $x=1$

Substitute $x=1$ into $f(x)=4800x+1200$:
$f(1)=4800(1)+1200=6000$
Gives the pair $(1, 6000)$

Step4: Calculate cost for $x=2$

Substitute $x=2$ into $f(x)=4800x+1200$:
$f(2)=4800(2)+1200=10800$
Gives the pair $(2, 10800)$

Step5: Calculate cost for $x=3$

Substitute $x=3$ into $f(x)=4800x+1200$:
$f(3)=4800(3)+1200=15600$
Gives the pair $(3, 15600)$

Answer:

$\{(0,1200),(1,6000),(2,10800),(3,15600)...\}$