Answer :
Let:
x = duration of each call
y = cost of the call
Since the cost of the call and the length of the call are related. we can model the situation as a linear equation of the form:
[tex]y=mx+b[/tex]a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86, so:
[tex]\begin{gathered} x=5,y=5.91 \\ so\colon \\ 5.91=5m+b \\ --------- \\ x=10,y=10.86 \\ so\colon \\ 10.86=10m+b \end{gathered}[/tex]Let:
[tex]\begin{gathered} 5m+b=5.91_{\text{ }}(1) \\ 10m+b=10.86_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (2)-(1) \\ 10m-5m+b-b=10.86-5.91 \\ 5m=4.95 \\ m=\frac{4.95}{5} \\ m=0.99 \end{gathered}[/tex]Replace the value of m into (1):
[tex]\begin{gathered} 5(0.99)+b=5.91 \\ 4.95+b=5.91 \\ b=5.91-4.95 \\ b=0.96 \end{gathered}[/tex]Therefore, the cost as a function of time is:
[tex]y(x)=0.99x+0.96[/tex]