The relationship between time in months and height in inches for Kylie's plant is represented by the equation y=12x. The relationship for Jane's plant is represented by the equation 2y=24x. Is there a time when the two plants are the same height?

Question

One way you can solve this problem is to graph the relationship between time and height for both plants on the same coordinate plane. To do that, we need to find a few points to graph. Complete the table below to show the height of Jane's plant at various times.
2y = 24x

Time in months (x) Height in inches (y)
2
4
5

Answer 1

To find the height of Jane's plant at various times based on the equation \(2y = 24x\), we first need to solve for \(y\):

\[ 2y = 24x \]

Dividing both sides by 2 gives:

\[ y = 12x \]

Now, we can create a table of values for \(y\) (height) at different values of \(x\) (time in months).

Table of Heights for Jane's Plant:

| Time in months (x) | Height in inches (y) | |---------------------|-----------------------| | 2 | \(y = 12(2) = 24\) | | 4 | \(y = 12(4) = 48\) | | 5 | \(y = 12(5) = 60\) |

Now we can summarize the heights of Jane's plant at the specified times:

• At 2 months, Jane's plant is 24 inches tall.
• At 4 months, Jane's plant is 48 inches tall.
• At 5 months, Jane's plant is 60 inches tall.

Since Kylie's plant is also represented by the same equation, \(y = 12x\), both Kylie's and Jane's plants grow at the same rate, indicating that they will always be the same height for the same value of \(x\).

Thus, there is never a time when the two plants are different heights, as they grow equally and are represented by the same equation for height.