The table shows the height of a plant as it grows. What equation in point-slope form gives the plant’s height at any time? Let y stand for the height of the plant in cm and let x stand for the time in months.
A. y – 15 = (x – 3)
B. y – 15 = 5(x – 3)
C. y – 3 = (x – 15)
D. The relationship cannot be modeled.
D
because you did not show the data ...
To determine the equation in point-slope form that gives the plant's height at any time, we need to analyze the given table. However, the table's information is missing from the question. Please provide the values from the table, and I will be able to assist you in identifying the correct equation.
To determine the equation in point-slope form that represents the relationship between the plant's height and time, we need to analyze the given data and identify the slope and a point on the line.
Looking at the options:
A. y – 15 = (x – 3)
B. y – 15 = 5(x – 3)
C. y – 3 = (x – 15)
D. The relationship cannot be modeled.
We can start by analyzing option A, y – 15 = (x – 3). This equation represents a linear relationship with a slope of 1. Moreover, it implies that for each unit increase in time (x), the height (y) increases by 1 unit. However, in the given data, there is no indication that the plant's height increases by a constant rate of 1 unit for each month. So, option A can be eliminated.
Next, let's check option B, y – 15 = 5(x – 3). This equation represents a linear relationship with a slope of 5. This suggests that for each unit increase in time (x), the height (y) increases by 5 units. This option could be plausible if the given data shows a consistent pattern of the plant's height increasing at a constant rate of 5 units for each month. However, without more information about the data, we cannot determine if this is the correct equation. So, let's keep option B as a possibility for now.
Now, let's analyze option C, y – 3 = (x – 15). This equation also represents a linear relationship, but with a slope of 1. This suggests that for each unit increase in time (x), the height (y) increases by 1 unit. Similarly to option A, this does not align with the given data since there is no indication of a constant rate of growth. Therefore, option C can be eliminated.
Based on the analysis so far, we can conclude that option D, "The relationship cannot be modeled," is unlikely the correct choice since we have identified a possible equation in option B.
To fully determine the correct equation, we would need more information about the given data. However, based on the options provided, option B, y – 15 = 5(x – 3), is the most plausible equation in point-slope form that represents the relationship between the plant's height and time.