School Event Bakery: Recipe Models

Build linear functions from recipes, records, and graphs.

Recipe Records

Assume each relationship is linear. Identify what changes per batch and what is already present when x = 0.

A bakery is scaling recipes for a school event. The table shows flour needed for its bread recipe.

Bread Recipe
Batches (x)	Flour, cups (y)
2	5
4	10
7	17.5

Find the rate of change: cups per batch. Find the initial value: cups.

Each batch of oatmeal bars needs 3/4 cup of oil. There is no additional oil used outside the batches. Which function gives the total oil y, in cups, for x batches?

A. y = x + 3/4B. y = (3/4)x + 1C. y = (3/4)xD. y = (4/3)x

For one baking session, Amara measures 1.5 cups of sugar for a shared glaze. Each batch of rolls needs another 2 cups of sugar. Let x be the number of batches and y be all the sugar measured, in cups.

Complete the function: y = x + .

The bakery records ingredients for a muffin recipe. The points (3, 5.25) and (8, 14) give (batches, cups of milk). Which function gives cups of milk y for x batches?

A. y = 8.75xB. y = 2.8xC. y = 1.75x + 5.25D. y = 1.75x

A butter supply is used only for batches of biscuits. Let x be batches prepared and y be cups of butter remaining.

Butter Supply
Batches (x)	Butter left, cups (y)
2	15
5	10.5
8	6

Complete the function using a signed rate: y = x + .

Graphs and Checkpoints

Use the plotted relationships and recorded points to build models. Pay attention to the meaning of each axis.

The bakery may increase or decrease its original bread order. Here x is the signed change in batches and y is the signed change in cups of flour. Negative values mean a decrease. Which function fits the graph?

A. y = 2xB. y = −2xC. y = x + 2D. y = (1/2)x

This graph shows the total cups of water y measured for x batches of dough. The total includes water for a single shared starter.

Complete the model: y = x + .

For a cookie recipe, x is the number of batches and y is the number of eggs needed. Two records are (4, 12) and (9, 27). Which statement correctly describes the linear model?

A. The rate is 3 eggs per batch, and the initial value is 0 eggs.B. The rate is 3 eggs per batch, and the initial value is 12 eggs.C. The rate is 5 eggs per batch, and the initial value is 12 eggs.D. The rate is 15 eggs per batch, and the initial value is 0 eggs.

A supply of raisins decreases at a constant rate as batches of scones are mixed. After 3 batches, 13 cups remain. After 7 batches, 7 cups remain. Let x be batches mixed and y be cups remaining.

The rate of change is cups per batch. Before any batches were mixed, there were cups.

Use and Check the Models

Build a linear model for each decision. Check that its rate and initial value match the situation.

10.

A standard batch of lemon bars uses 1.25 cups of lemon juice. For the school event, each batch will be three times as large. A separate display dessert needs 2 cups of juice, regardless of the number of batches. Which model gives total juice y, in cups, for x event-size batches?

A. y = 5.75xB. y = 3.75x + 2C. y = 1.25x + 6D. y = 3.75x + 6

11.

The bakery has 23 cups of oats. It reserves 3 cups for a topping and uses 2.5 cups for each batch of breakfast bars. Let x be batches and y be total cups of oats needed.

Complete the model: y = x + . The greatest number of whole batches it can make is .

12.

Each batch of cinnamon rolls needs the same amount of icing. One extra cup is also prepared for a tasting tray. The table includes this extra cup.

Icing to Prepare
Batches (x)	Total icing, cups (y)
2	4
6	?
10	16

Complete the function: y = x + 1. How many cups belong in the missing table entry? cups.

13.

The bakery prepares one fixed bowl of fruit sauce for the school's tasting table. The amount of sauce does not depend on how many batches of pastries are baked.

Tasting-Table Sauce
Pastry batches (x)	Sauce, cups (y)
2	6
5	6
9	6

Mateo writes y = 6x because every row shows 6 cups. Explain why his model does not fit. State the correct function, its rate of change, and its initial value.