Question

determining the rate of change of a line on a graph
the graph shows the height of a tree over time. what can you deduce the rate of change to be from 2 years to 4 years?
○ 2 inch per year
○ 2.5 inches per year
○ 5 inches per year
○ 10 inches per year

Explanation:

Step1: Identify two points

From the graph, at \( x = 2 \) (2 years), \( y = 5 \) inches (height). At \( x = 4 \) (4 years), \( y = 10 \) inches (height).

Step2: Calculate rate of change

Rate of change (slope) formula: \( \frac{y_2 - y_1}{x_2 - x_1} \)
Substitute values: \( \frac{10 - 5}{4 - 2} = \frac{5}{2} = 2.5 \) inches per year.

Answer:

2.5 inches per year (corresponding to the option "2.5 inches per year")