Question

A bean plant grows at a constant rate for a month. After 10 days, the plant is 25 centimeters tall. After 20 days, the plant is 45 centimeters tall. Which equation models the height of the plant, y, after x days?

Answer 1

The height of the bean plant after x days is modeled by the linear equation y = 2x + 5, where y represents the height in centimeters and x represents the days.

Step-by-step explanation:

Linear Equation for Plant Growth

To model the height of the plant, y, after x days, we can create a linear equation based on the information provided:

After 10 days, the plant is 25 centimeters tall.

After 20 days, the plant is 45 centimeters tall.

First, we calculate the rate of growth per day by subtracting the height of the plant at 10 days from the height at 20 days, then dividing by the number of days:

Rate of growth = (45 cm - 25 cm) / (20 days - 10 days) = 20 cm / 10 days = 2 cm/day

Then, we find the initial height (y-intercept) of the plant at day 0 using one of the points, like (10, 25):

25 cm = 2 cm/day * 10 days + initial height

Initial height = 25 cm - 20 cm = 5 cm

The equation modeling the height of the plant after x days is:

y = 2x + 5

Answer 2

y = 2x + 5

If you take the height at 10 days, 25 centimeters, after 10 more days the height is 45 centimeters, meaning for those 10 extra days the been plant grown 20 centimeters. Since we're told the plant is growing at a constant rate, this shows the bean plant is growing 2 centimeters per day. We can represent this with y = 2x. (After 10 days, the bean plant will be 20 centimeters, after 20 days, the bean plant will be 40 centimeters, etc.)

However, this is not completely true yet. As you can see, after the first 10 days the plant is not 20 centimeter, it's 25 centimeters. We already know the rate in which the plant is changing, but now we need to find the height that the plant was originally, before it started growing.

After the first 10 days, the plant is 25 centimeters tall. Since we know that the plant is growing 2 centimeters per day, we can subtract 20 from 25 to find the original height of the bean plant.

25 - 20 = 5
The bean plant was originally 5 centimeters.

This makes our final equation y = 2x + 5.
2x is the slope, and 5 is the y intercept.

Hope this helps1!