(1 point)
State sales tax $y$ is directly proportional to retail price $x$. An item that sells for 186 dollars has a sales tax of 10.22 dollars. Find a mathematical model that gives the amount of sales tax $y$ in terms of the retail price $x$.
Your answer is $y=$
What is the sales tax on a 340 dollars purchase.
Your answer is:

Step 1 ：The problem states that the sales tax $y$ is directly proportional to the retail price $x$. This means that the relationship between $y$ and $x$ can be expressed as $y=kx$, where $k$ is the constant of proportionality.

Step 2 ：We can find the value of $k$ by substituting the given values of $y$ and $x$ into the equation. Given that an item that sells for 186 dollars has a sales tax of 10.22 dollars, we substitute these values into the equation to get $10.22=k\times 186$.

Step 3 ：Solving for $k$, we get $k=\frac{10.22}{186}=0.054946236559139786$.

Step 4 ：Now that we have the value of $k$, we can use it to find the sales tax on a 340 dollars purchase. Substituting $x=340$ into the equation $y=kx$, we get $y=0.054946236559139786\times 340=18.68172043010753$.

Step 5 ：Rounding to the nearest cent, the sales tax on a 340 dollars purchase is $\boxed{{\displaystyle 18.68}}$ dollars.