Question

brandon buys an english ivy plant to decorate the shelf in his bedroom. the ivy grows over time.
this situation can be modeled as a linear relationship.
what does the slope of the line tell you about the situation?
the ivy grows 1 inch every 6 months.
the ivy grows 2 inches every 9 months.
the ivy grows 6 inches every month.
the ivy grows 9 inches every 2 months.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line. From the graph, we can take the points \( (0,6) \) (when \( x = 0 \), \( y=6 \)) and \( (10,54) \) (when \( x = 10 \), \( y = 54 \)).

Step2: Calculate the slope

Using the slope formula: \( m=\frac{54 - 6}{10 - 0}=\frac{48}{10} = 4.8 \)? Wait, no, maybe better to take another pair. Wait, let's check the options. Let's take \( (0,6) \) and \( (2,15.6) \)? No, wait the options are about growth over time. Wait, let's check the option "The ivy grows 9 inches every 2 months". Let's see, from \( x = 0 \), \( y=6 \); at \( x = 2 \), what's \( y \)? Wait the line: when \( x = 0 \), \( y=6 \); when \( x = 2 \), let's see the grid. Wait the y - axis is length in inches, x - axis time in months. Let's take two points: \( (0,6) \) and \( (2, 15) \)? No, wait the option "The ivy grows 9 inches every 2 months". Let's check the slope between \( x = 0 \), \( y=6 \) and \( x = 2 \), \( y=6 + 9=15 \)? Wait no, maybe miscalculation. Wait the correct option: let's check the slope. Let's take \( (0,6) \) and \( (2, 15) \)? No, wait the option "The ivy grows 9 inches every 2 months" means slope \(=\frac{9}{2}=4.5 \). Wait let's check with \( (0,6) \) and \( (10,54) \): \( \frac{54 - 6}{10 - 0}=\frac{48}{10}=4.8 \), close to 4.5. Wait maybe the points are \( (0,6) \) and \( (2, 15) \): \( \frac{15 - 6}{2 - 0}=\frac{9}{2}=4.5 \). So the slope is \( \frac{9}{2} \), which means for every 2 months (change in x = 2), the change in y (length) is 9 inches. So the correct option is "The ivy grows 9 inches every 2 months".

Answer:

The ivy grows 9 inches every 2 months.