Question

The growth of a Brinjal plant in the garden is recorded over a period of 5 days in the following table. Does it follow a proportional relationship? If so, what is the proportional relationship?
day1 brinjal 0.75in day2 brinjal1.50in day3 brinjal 2.25in day4 brinjal 3.0in day5 brinjal 3.75in
Yes, y = 0.75x where "x" is the number of days
Yes, y = 1x where "x" is the number of days
Yes, y = 0.5x where "x" is the number of days
No

Answer 1

To determine if the growth of the Brinjal plant follows a proportional relationship, we can examine the data provided:

- Day 1: 0.75 in
- Day 2: 1.50 in
- Day 3: 2.25 in
- Day 4: 3.0 in
- Day 5: 3.75 in

We can express the height of the plant in terms of the number of days \( x \).

Let's summarize the relationship between the number of days \( x \) and the height of the brinjal plant \( y \):

- For Day 1 (x=1), y = 0.75
- For Day 2 (x=2), y = 1.50
- For Day 3 (x=3), y = 2.25
- For Day 4 (x=4), y = 3.00
- For Day 5 (x=5), y = 3.75

Next, we can observe that as \( x \) increases, \( y \) increases in a regular manner. To check if the relationship is proportional, we can find the constant ratio \( \frac{y}{x} \) for each day:

- For Day 1: \( \frac{0.75}{1} = 0.75 \)
- For Day 2: \( \frac{1.50}{2} = 0.75 \)
- For Day 3: \( \frac{2.25}{3} = 0.75 \)
- For Day 4: \( \frac{3.00}{4} = 0.75 \)
- For Day 5: \( \frac{3.75}{5} = 0.75 \)

The ratio \( \frac{y}{x} \) is constant at \( 0.75 \) for each day. This indicates a proportional relationship.

Thus, we can express the relationship as:
\[ y = 0.75x \]

Where \( y \) represents the height in inches and \( x \) is the number of days.

So the answer is:
**Yes, y = 0.75x where "x" is the number of days.**