a. Since the cost, in dollars, is 47 for 260 minutes, we have:
[tex]\begin{gathered} y=mx+b \\ 47=260m+b \end{gathered}[/tex]
Also, since the cost, in dollars, is 108 for 870 minutes, we have:
[tex]108=870m+b[/tex]
Now, subtracting the first equation from the second, we obtain:
[tex]\begin{gathered} 108-47=870m+b-260m-b \\ \\ 61=610m \\ \\ m=\frac{61}{610} \\ \\ m=0.1 \end{gathered}[/tex]
Now, we can use this result to find the value of b:
[tex]\begin{gathered} 108=870\cdot0.1+b \\ \\ b=108-87 \\ \\ b=21 \end{gathered}[/tex]
Therefore, the equation is:
[tex]y=\mathbf{0.1x+21}[/tex]
b. Now, we need to find y for x = 894. We have:
[tex]\begin{gathered} y=0.1\cdot894+21 \\ \\ y=89.4+21 \\ \\ y=110.4 \end{gathered}[/tex]
Thus, the answer is:
If 894 minutes are used, the total cost will be 110.4 dollars.
