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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?

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
You got it!
Now, graph the points that you just found to show the relationship between time in months and height in inches for Jane's plant.
Time in months (x) Height in inches (y)
2 24
4 48
5 60
Nice!
Next, consider the height of Kylie's plant, represented by the equation below. Complete the table below to show the height of Kylie's plant at various times.
y = 12x

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

1 answer

To find the height of Kylie's plant using the equation \(y = 12x\), we can substitute the values of \(x\) (time in months) into the equation. Here are the calculations for each \(x\):

  1. For \(x = 2\): \[ y = 12(2) = 24 \]

  2. For \(x = 4\): \[ y = 12(4) = 48 \]

  3. For \(x = 5\): \[ y = 12(5) = 60 \]

Now we can fill in the table for Kylie's plant:

Time in months (x) | Height in inches (y)

  • 2 | 24
  • 4 | 48
  • 5 | 60

Summary of Heights:

  • At \(x = 2\) months, Kylie's plant is 24 inches tall.
  • At \(x = 4\) months, Kylie's plant is 48 inches tall.
  • At \(x = 5\) months, Kylie's plant is 60 inches tall.

Comparing Heights of Both Plants:

Now, let's consider the height of Jane's plant for the same times:

  1. At \(x = 2\) months, Jane's plant is 24 inches tall. (They are the same height!)
  2. At \(x = 4\) months, Jane's plant is 48 inches tall. (They are the same height!)
  3. At \(x = 5\) months, Jane's plant is 60 inches tall.

Conclusion:

Yes, there is a time when the two plants are the same height, which occurs at both 2 months and 4 months, where both plants reach 24 inches and 48 inches, respectively. The plants are both 60 inches tall after 5 months.