Question

exit ticket name ____ date __ pd __ julie is tracking the growth of a plant for a science project. the height of the plant on the 2nd day she measured was 8 inches and on the 7th day it was 20.5 inches. assume the relationship is linear. step 1: find and interpret the rate of change. step 2: find the initial value. step 3: write an equation for the function.

Explanation:

Step1: Define linear data points

Let $x$ = day, $y$ = height (in). Points: $(2, 8)$ and $(7, 20.5)$

Step2: Calculate rate of change

Rate of change = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{20.5 - 8}{7 - 2} = \frac{12.5}{5} = 2.5$
Interpretation: Plant grows 2.5 inches/day.

Step3: Solve for initial value ($b$)

Use $y = mx + b$, $m=2.5$, point $(2,8)$:
$8 = 2.5(2) + b$
$8 = 5 + b$
$b = 8 - 5 = 3$

Step4: Write linear function

Substitute $m=2.5$, $b=3$ into $y=mx+b$:
$y = 2.5x + 3$

Answer:

1. Rate of change: 2.5 inches per day; the plant grows 2.5 inches each day.
2. Initial value: 3 inches (the plant's height on day 0).
3. Function equation: $y = 2.5x + 3$ where $x$ is the number of days and $y$ is the plant's height in inches.