Question

Each day Julian gives his dog, Banjo, 3 liters of water and 500 grams of food. Julian wants to track the total amount of the food and water he gives Banjo for one week. Julian plots a point at (3, 500) to represent the first day on a coordinate grid. Then Julian uses a pattern to plot six more points. Describe the pattern of the points that represent the total amount food and water Julian gives Banjo in one week. Enter your answers in the boxes to complete the pattern. (1 point) Each day, the x-coordinate increases by , and the y-coordinate increases by Remaining Attempts : 3 Skip to navigation

Answer 1

To determine the pattern for the points that represent the total amount of food and water Julian gives Banjo over one week, we can examine the data provided.

Each day, Julian gives:
- Water: 3 liters
- Food: 500 grams

Over one week (which is 7 days), the amount of water and food given to Banjo will accumulate.

### For the x-coordinate:
Each day represents a day, so the x-coordinate will start at 3 (for the first day) and increase by 1 for each subsequent day. Thus:
- Day 1 (x=1): (3, 500)
- Day 2 (x=2):
- Day 3 (x=3):
- Day 4 (x=4):
- Day 5 (x=5):
- Day 6 (x=6):
- Day 7 (x=7):

The x-coordinate increases by **1** each day.

### For the y-coordinate:
Each day, Banjo receives 3 liters of water and 500 grams of food. Over 7 days, we can calculate the total as follows:
- Water for 7 days = \(3 \times 7 = 21\) liters
- Food for 7 days = \(500 \times 7 = 3500\) grams

The total amount of food and water would be represented by:
- Total water (in grams) = \(21 \text{ liters} = 21 \times 1000 = 21000 \text{ grams}\) (if combining food and water in grams)
- Total food = 3500 grams

Converted, the total (in grams) becomes \(21000 + 3500 = 24500\) grams.

However, the points themselves will evolve as follows from the first day:
- For Day 2 (x=2): y-coordinate = \(3 \times 2 + 500 \times 2 = 6 + 1000 = 1006\)
- For Day 3 (x=3): y-coordinate = \(3 \times 3 + 500 \times 3 = 9 + 1500 = 1509\)

Continuing this for the other days, the y-coordinate also increases consistently:
- Each day contributes an additional 3 liters + 500 grams to the total from the previous day.

So:
- The y-coordinate increases by \(3 + 500 = 503\) grams each day.

### Final Pattern Description:
- Each day, the x-coordinate increases by **1**.
- Each day, the y-coordinate increases by **503** grams.