$19.47
1) Examining the graph, we can write two coordinate pairs the x-coordinate for the minutes and the y-coordinate for the cost. So we have (54, 17.04) and (86, 19.92) so we can find from that the rule of this function. Let's find the slope of it:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{19.92-17.04}{86-54}=0.09[/tex]
Note that the slope shows how steep is the line of that function.
2) Let's find the linear coefficient, where the graph intercepts the y-axis.
Writing the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ \mleft(54,17.04\mright) \\ 17.04=0.09(54)+b \\ 17.04-4.86=b \\ b=12.18 \end{gathered}[/tex]
So the rule of this function is:
[tex]f(x)=0.09x+12.18[/tex]
3) Now we can find out the answer, by plugging into that equation x=81
[tex]\begin{gathered} f(81)=0.09(81)+12.18 \\ f(81)=19.47 \end{gathered}[/tex]
Thus, the monthly cost for 81 minutes is $19.47
