The relationship between time in months and height in inches for Oliver's plant is represented by the equation y=5x. The relationship for Madison's plant is represented by the equation 2y=10x. 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 Madison's plant at various times.
2y = 10x

Time in months (x) Height in inches (y)
2
4
6

Answer 1

To find the height of Madison's plant using the equation \(2y = 10x\), we first need to simplify this equation to express \(y\) in terms of \(x\):

\[ y = \frac{10x}{2} \] \[ y = 5x \]

Now we can see that the height of Madison's plant also follows the same relationship as Oliver's plant, which is \(y = 5x\).

Now, let's complete the table for Madison's plant at various time intervals:

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

1. For \(x = 2\): \[ y = 5 \times 2 = 10 \]

2. For \(x = 4\): \[ y = 5 \times 4 = 20 \]

3. For \(x = 6\): \[ y = 5 \times 6 = 30 \]

Now, filling in the table:

| Time in months (x) | Height in inches (y) | |---------------------|-----------------------| | 2 | 10 | | 4 | 20 | | 6 | 30 |

Conclusion:

Since both equations (for Oliver's and Madison's plants) are identical (\(y = 5x\)), the heights of both plants will be the same for any given time. Therefore, at any month \(x\), both plants will have the same height.