Given the following prices:
In-Store Price Online Price
$50.00 $45.00
$75.00 $67.50
$100.00 $90.00
To determine if the online price vary directly with the in-store price, let's find the constant of proportionality.
Let y = online price
Let x = In-store price
Where y varies directly as x, we have:
y = kx
45 = 50k
[tex]\begin{gathered} \frac{45}{50}=\frac{50k}{50} \\ \\ 0.9=k \end{gathered}[/tex]Since constant of proportionality, k = 0.9, let's determine if there is a direct variation using the second and third prices on the list.
y = kx
y = 0.9(75) = 67.5
y = kx
y = 0.9(100) = 90
[tex]k=\frac{45}{50}=\frac{67.5}{75}=\frac{90}{100}=0.9[/tex]Therefore, we can say that the online price varies directly with the in-store price. This is because they have the same constant of proportionality.
ANSWER:
Yes, the online price varies directly with the in-store price.
