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:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Here, the graph passes through (2, 44) and (4, 88). So, the equation of the graph is:
[tex]\begin{gathered} y-44=\frac{88-44}{4-2}(x-2) \\ y-44=\frac{44}{2}(x-2) \\ y-44=22(x-2) \\ y-44=22x-44 \\ y=22x-44+44 \\ y=22x \end{gathered}[/tex]
Here, the equation of the line is y = 22x.
Thus, the constant of proportionality is 22.
