Question

The graph below represents the price of sending picture messages using the services of a phone company. What is the constant of proportionality?

Answer 1

Given:

A graph showing price of sending pictures messages using the service of a phone company.

To find:

The constant of proportionality.

Solution:

If the equation of the graph has the form y = kx, then k is the proportionality constant.

It is known that the equation of the line passing through two points (x1, y1) and (x2, y2) is given by:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Here, the graph passes through (2, 44) and (4, 88). So, the equation of the graph is:

`\begin{gathered} y-44=(88-44)/(4-2)(x-2) \\ y-44=(44)/(2)(x-2) \\ y-44=22(x-2) \\ y-44=22x-44 \\ y=22x-44+44 \\ y=22x \end{gathered}`

Here, the equation of the line is y = 22x.

Thus, the constant of proportionality is 22.