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
Good work!
Now, graph the points that you just found to show the relationship between time in months and height in inches for Madison's plant.
Time in months (x) Height in inches (y)
2 10
4 20
6 30
Nice!
Next, consider the height of Oliver's plant, represented by the equation below. Complete the table below to show the height of Oliver's plant at various times.
y = 5x

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

Answer 1

To find the height of Oliver's plant at various times based on the equation \( y = 5x \), we can plug in the values for time (x) into the equation.

Here’s the completed table for Oliver's plant:

Time in months (x) | Height in inches (y) --- | --- 2 | \( y = 5 \times 2 = 10 \) 4 | \( y = 5 \times 4 = 20 \) 6 | \( y = 5 \times 6 = 30 \)

So the table for Oliver's plant looks like this:

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

Now you can see that for both plants, the heights at 2, 4, and 6 months are identical:

• At 2 months: Oliver's plant is 10 inches, Madison's plant is 10 inches.
• At 4 months: Oliver's plant is 20 inches, Madison's plant is 20 inches.
• At 6 months: Oliver's plant is 30 inches, Madison's plant is 30 inches.

Thus, the two plants are the same height at all of these times (2, 4, and 6 months).