Given:
c = total cost.
s = number of songs.
To solve this question, follow the steps below.
Step 01: Find 2 points (s, c).
You can choose 2 points from the table.
Let's choose (14, 8.96) and (16, 10.24).
Step 02: Substitute one point in the general equation.
Given the general equation:
[tex]c=ms+b[/tex]
Substituting the first point.
[tex]\begin{gathered} 8.96=14m+b \\ 8.96-14m=b \\ b=8.96-14m \end{gathered}[/tex]
Isolating b by subtracting 8.96 m from both sides:
[tex]\begin{gathered} 14-8.96m=8.96m+b-8.96m \\ 14-8.96m=b \\ b=14-8.96m \end{gathered}[/tex]
Step 03: Substitute b in the general equation.
[tex]\begin{gathered} c=ms+b \\ c=ms+8.96-14m \end{gathered}[/tex]
Step 04: Substitute the second point in the equation above.
[tex]\begin{gathered} c=ms+8.96-14m \\ 10.24=16m+8.96-14m \\ 10.24=2m+8.96 \end{gathered}[/tex]
Step 05: Solve the equation above for m.
To do it, first, subtract 8.96 from both sides.
[tex]\begin{gathered} 10.24-8.96=2m+8.96-8.96 \\ 1.28=2m \end{gathered}[/tex]
Now, divide both sides by 2.
[tex]\begin{gathered} \frac{1.28}{2}=\frac{2}{2}m \\ m=0.64 \end{gathered}[/tex]
Step 06: Substitute m in the equation from step 02 to find b.
[tex]\begin{gathered} b=8.96-14m \\ b=8.96-14\cdot0.64 \\ b=8.96-8.96 \\ b=0 \end{gathered}[/tex]
Step 07: Write the equation.
[tex]\begin{gathered} c=0.64s+0 \\ c=0.64s \end{gathered}[/tex]
Answer:
c = 0.64s
