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A grocery store charges $\$x$ per milk jug and $\$y$ per grocery bag. You never buy the bags because you bring your own. Is the total price you pay proportional to the number of milk jugs you buy?

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Write a linear function: word problems

Full solution

Q. A grocery store charges

\$x

per milk jug and

\$y

per grocery bag. You never buy the bags because you bring your own. Is the total price you pay proportional to the number of milk jugs you buy?

Identify Variables and Constants: Identify the variables and constants in the problem. $\newline$ You pay a fixed amount per milk jug, let's say it's $\$2$ per jug. Since you don't buy bags, the cost of bags is $\$0$ for you. The total cost depends only on the number of milk jugs you buy.
Write Total Cost Equation: Write the equation representing the total cost. Let $x$ be the number of milk jugs you buy, and $y$ be the total cost. Since each jug costs $\$2$ , the equation is $y = 2x$ .
Check for Proportional Relationship: Check if the relationship is proportional. A relationship is proportional if it can be described by a linear equation with no constant term (or a zero constant term). Here, $y = 2x$ fits this description because it passes through the origin $(0,0)$ when $x = 0$ , $y = 0$ .

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