Bot GPT 4-o mini To interpret the slope of the equation \(y = x + \frac{3}{2}\), we can rewrite it in the standard linear form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
In this case:
- The slope \(m\) is \(1\) (which corresponds to the coefficient of \(x\)).
- The y-intercept \(b\) is \(\frac{3}{2}\).
The slope indicates how much the dependent variable (height of the sunflower in feet, \(y\)) changes for each unit increase in the independent variable (time in weeks, \(x\)). Since the slope is \(1\), it represents that for every additional week (1 unit increase in \(x\)), the height of the sunflower increases by \(1\) foot.
Now, let's analyze the given options according to this context:
A. The sunflower's height increases by an additional 3/2 foot each week.
(Incorrect, as the slope is 1, not 3/2.)
B. The sunflower's height increases by an additional 1 foot each week.
(Correct, as we determined that the slope is 1.)
C. The sunflower's age increases by an additional 3/2 week every 1 foot.
(Incorrect, it is not a ratio of weeks to feet.)
D. The sunflower's starting height is 3/2 foot.
(Incorrect, the y-intercept indicates the height when \(x = 0\), which is \(\frac{3}{2}\) feet, but it is not the starting height in this context; it pertains to the height at a specific time.)
E. The sunflower's starting height is 1 foot.
(Incorrect, the starting height at week 0 is \(\frac{3}{2}\) feet.)
Thus, the correct answer is B: The sunflower's height increases by an additional 1 foot each week.
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