Question

Steven recorded the growth of a plant over 10 weeks for his science project. He made a graph that shows how much the plant grew each week. The plant was 2 in. tall when Steven started his project. At week 5, the plant was 8 in. tall. Which equation represents Steven’s situation, where x is the number of weeks and y is the height of the plant? Responses y=56x+2 y equals fraction 5 over 6 end fraction x plus 2 y=65x+2 y equals fraction 6 over 5 end fraction x plus 2 y=85x+2 y equals fraction 8 over 5 end fraction x plus 2 y=58x+2

Answer 1

Both y = 8/5x + 2 and y = 58x + 2 represent possible linear relationships between plant height and weeks, depending on remaining data points or experiment context.

We need to find the equation that represents the linear relationship between the plant's height (y) and the number of weeks (x), considering the initial height and the height at week 5.

Here's the analysis of each option:

y = 56x + 2: This equation implies a much steeper growth rate than the given information. The plant wouldn't reach 8 inches by week 5 with this slope.

y = 5/6x + 2: This equation suggests a very gradual growth, unlikely to reach 8 inches in 5 weeks.

y = 65x + 2: This equation leads to an even steeper growth than 56x + 2, making it implausible.

y = 8/5x + 2: This equation yields a more realistic growth rate. With this slope, the plant could reach 8 inches by week 5.

y = 58x + 2: This equation results in a slightly steeper growth than 8/5x + 2, but it could still be a valid representation depending on the actual data points.

Therefore, the most likely equation representing Steven's situation is y = 8/5x + 2 or y = 58x + 2. Further analysis of the remaining data points or the specific context of the experiment could help determine the exact equation.