A chef is ordering ingredients to make spaghetti sauce. This table shows the proportional relationship between x, the amount of tomatoes she orders in pounds, and y, the cost of the tomatoes in dollars.

Question

(x) (y)
31, 31
44, 44
70, 70
92, 92
Write an equation for the relationship between x and y.

Answer 1

The relationship between the amount of tomatoes ordered (x) and their cost (y) is proportional, which means that the cost is directly proportional to the amount of tomatoes.

From the table, you can see that for each value of x, the value of y is equal to x. This suggests that the constant of proportionality (k) is 1.

The equation for this relationship can be written as:

\[ y = k \cdot x \]

Since \( k = 1 \), the equation simplifies to:

\[ y = 1 \cdot x \] or simply: \[ y = x \]

Thus, the equation representing the relationship between the amount of tomatoes ordered (x) and the cost of the tomatoes (y) is:

\[ y = x \]