When you receive Plant A, it is 4 cm tall and grows at a constant rate of 2 cm per month. When you receive Plant C, it is 8 cm tall and grows at a constant rate of 2 cm per month.

Question

How can you use the graph to determine that the plants will never be the same height?
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The lines are
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Answer 1

To determine whether Plant A and Plant C will ever be the same height using a graph, you can plot their growth over time on a coordinate system where the x-axis represents time (in months) and the y-axis represents height (in centimeters).

1. Define Height as a Function of Time:

   • For Plant A: The height \( h_A \) as a function of time \( t \) can be expressed as: \[ h_A = 4 + 2t \]
   • For Plant C: The height \( h_C \) as a function of time \( t \) can be expressed as: \[ h_C = 8 + 2t \]

2. Plot the Growth on the Graph:

   • Start with Plant A, which is initially at 4 cm (when \( t = 0 \)) and grows at a rate of 2 cm per month. The line for Plant A starts at (0, 4) and has a slope of 2.
   • For Plant C, start at 8 cm (when \( t = 0 \)) and also grows at a rate of 2 cm per month. The line for Plant C starts at (0, 8) and also has a slope of 2.

3. Analyzing the Lines:

   • Both plants have the same growth rate (2 cm per month), which means that their rate of increase in height is identical. This results in parallel lines on the graph.
   • Since Plant A starts at 4 cm and Plant C starts at 8 cm, the distance between the two lines remains constant as they grow.

4. Conclusion:

   • Because the lines are parallel, they will never intersect, which means that the heights of Plant A and Plant C will never be the same, regardless of how much time passes.

So, to summarize: The lines are parallel, so there will never be a point where the heights of Plant A and Plant C are the same.