Question

1. lila planted a tree in her backyard. she made this over 5 years.

a. what is the y-intercept? ______ describe what it means in the context of the problem.
b. what is the slope? ______ describe what it means in the context of the problem

Explanation:

Step1: Identify y-intercept (x=0)

The y-intercept is the point where $x=0$. From the graph, this is $(0, 5)$.

Step2: Interpret y-intercept context

At year 0 (planting time), height is 5 ft.

Step3: Calculate slope using two points

Use points $(0,5)$ and $(5,20)$. Slope formula: $\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$
$\text{slope} = \frac{20 - 5}{5 - 0} = \frac{15}{5} = 3$

Step4: Interpret slope context

Slope is annual height increase.

Answer:

a. The y-intercept is 5. This means when Lila planted the tree (Year 0), the tree was 5 feet tall.
b. The slope is 3. This means the tree grows 3 feet every year.