A) The constant of proportionality in this proportional relationship is [tex]k = \frac{y}{x}[/tex]
B) The equation to represent this proportional relationship is y = 0.3x
Solution:
Given that, the amount she pays each month for international text messages is proportional to the number of international texts she sends that month
Therefore,
This is a direct variation proportion
[tex]\text{ amount Naomi pays each month } \propto \text{ number of international texts she sends that month}[/tex]
Let "y" be the amount that Naomi pays each month
Let "x" be the number of international texts she sends that month
Therefore,
[tex]y \propto x[/tex]
y = kx -------- eqn 1
Where, "k" is the constant of proportionality
Thus the constant of proportionality in this proportional relationship is:
[tex]k = \frac{y}{x}[/tex]
Last month, she paid $7.20 for 24 international texts.
Therefore,
y = $ 7.20
x = 24
Thus from eqn 1,
[tex]7.20 = k \times 24\\\\k = \frac{7.20}{24}\\\\k = 0.3[/tex]
Substitute k = 0.3 in eqn 1
y = 0.3x
Thus the equation to represent this proportional relationship is y = 0.3x
