Question

Use the table to answer the question.

x (time in years) 0 2 4
y (height of tree in feet) 3 6 9
Interpret the y-intercept and slope in the context of this situation. For the slope, give the most simplified rate using whole numbers.(2 points)
The y-intercept is
feet. The slope is
feet every
year(s).

Answer 1

In the given context, \( y \) represents the height of a tree in feet, and \( x \) represents the time in years.

1. **Y-intercept:**
The y-intercept occurs when \( x = 0 \). From the table, when \( x = 0 \), \( y = 3 \).
Therefore, the y-intercept is **3 feet**. This means that at the start (0 years), the height of the tree is 3 feet.

2. **Slope:**
To calculate the slope, we can look at the change in height of the tree for each 2-year interval. From the table, the height of the tree increases from 3 feet to 6 feet (an increase of 3 feet) over 2 years, and from 6 feet to 9 feet (again an increase of 3 feet) over the next 2 years.

The slope (rate of growth) can be calculated as follows:
\[
\text{slope} = \frac{\text{change in height}}{\text{change in time}} = \frac{3 \text{ feet}}{2 \text{ years}} = \frac{3}{2} \text{ feet per year} = 1.5 \text{ feet per year}
\]

To express the slope in whole numbers, we can state it as **3 feet every 2 years**.

Final interpretation:
- The y-intercept is **3 feet**.
- The slope is **3 feet every 2 year(s)**.