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.

the y-intercept is _ feet. the slope is _ feet every _ year(s)

Answer 1

To interpret the y-intercept and slope using the data provided:

### Y-Intercept
The y-intercept occurs when x = 0. According to the table, when x = 0 years, the height of the tree (y) is 3 feet. Thus,

**The y-intercept is 3 feet.**

### Slope
The slope can be calculated using the change in height (y) over the change in time (x). We can use the points given in the table to find the slope:

From the data:
- When x = 0 years, y = 3 feet
- When x = 2 years, y = 6 feet
- When x = 4 years, y = 9 feet

Using two points, let’s take (0, 3) and (2, 6):

1. Change in y (height) = 6 - 3 = 3 feet
2. Change in x (time) = 2 - 0 = 2 years

Thus, the slope (m) is given by:

\[
m = \frac{\text{Change in } y}{\text{Change in } x} = \frac{3 \text{ feet}}{2 \text{ years}} = \frac{3}{2} \text{ feet per year}
\]

To express this in whole number terms, it simplifies to:

**The slope is 3 feet every 2 year(s).**

### Final Response:
The y-intercept is **3 feet**, and the slope is **3 feet every 2 year(s)**.