Question

he graph given shows the cost of sandwiches at a sandwich shop.



In the graph, y represents the cost of sandwiches and x represents the number of sandwiches sold. Which equation describes the proportional relationship between the cost of sandwiches and the number of sandwiches sold?

Answer 1

To determine the equation that describes the proportional relationship between the cost of sandwiches (y) and the number of sandwiches sold (x), we generally look for a linear relationship in the form of:

\[ y = kx \]

where \( k \) is the constant of proportionality, representing the cost per sandwich.

To find \( k \), you can select two points from the graph that you have, which should represent the cost (y) and the number of sandwiches sold (x). Then you can calculate \( k \) using the formula:

\[ k = \frac{y}{x} \]

For instance, if from the graph, you noticed that when 1 sandwich is sold, it costs $5, and when 2 sandwiches are sold, it costs $10, you would have:

- At \( x = 1 \), \( y = 5 \): \( k = \frac{5}{1} = 5 \)
- At \( x = 2 \), \( y = 10 \): \( k = \frac{10}{2} = 5 \)

This would give you the equation:

\[ y = 5x \]

If you can provide the specific points or details from the graph, I could help to find the exact equation for that situation.