Question

this question has two parts. use the information to answer part a and part b.
the graph shows the height of tree a over time.
the height of tree b can be represented by the equation ( y = 5x + 3 ) where ( x ) represents time in years, and ( y ) represents height in feet.
part a
which tree starts at a taller height?
a. tree a
b. tree b
c. they start at the same height.
part b
which tree grows at a faster rate?
a. tree a
b. tree b
c. they grow at the same rate.

Explanation:

Step1: Find Tree A's starting height

From the graph, at $x=0$ (time=0), height $y=5$ feet.

Step2: Find Tree B's starting height

For Tree B's equation $y=5x+3$, substitute $x=0$:
$y=5(0)+3=3$ feet.

Step3: Compare starting heights

$5 > 3$, so Tree A starts taller.

Step4: Find Tree A's growth rate

Calculate slope of Tree A's line: $\frac{\text{Change in } y}{\text{Change in } x} = \frac{35-5}{10-0} = \frac{30}{10}=3$ feet/year.

Step5: Find Tree B's growth rate

In $y=5x+3$, the coefficient of $x$ is 5, so growth rate is 5 feet/year.

Step6: Compare growth rates

$5 > 3$, so Tree B grows faster.

Answer:

Part A: A. Tree A
Part B: B. Tree B