Question

The table below shows the cost of downloading songs from a website. a Number of Songs Total Cost 14 $12.74 16 $14.56 18 $16.38 If e represents the total cost in dollars and cents for any number of songs downloaded, s, write a proportional equation for e in terms of s that matches the context.

Answer 1

From the question, the given table is

The table represents a linear function

Hence

To find the proportional equation for c in terms of s

The equation will be in the form

$y=mx+c$

From the table

When s = 14, c = $12.74

When s = 16, c = $14.56

Hence the slope of the line is

$m=\frac{14.56-12.74}{16-14}$

Simplifying this gives

$\begin{gathered} m=\frac{1.82}{2} \\ m=0.91 \end{gathered}$

Consider the values

When s = 14, c= $12.74

Using a point slope formula

$y-y_1=m(x-x_1)$

It follows

The equation for c in terms of s is

$c-12.74=0.91(s-14)$

Simplifying the equation gives

$\begin{gathered} c-12.74=0.91s-12.74 \\ c=0.91-12,74+12.74 \\ c=0.91s \end{gathered}$