Question

karla planted a queen palm tree in her backyard in 2016. when she planted it, it was 7.5 feet tall. the tree grew at a constant rate. by 2022, the tree was 21 feet tall. which linear equation models the situation? i do not know the answer yet y = 2.25x + 21 y = 2.25x + 7.5 y = 2.25x + 2016 y = 2.25x + 2016 y = 7.5x + 21

Explanation:

Step1: Define variables and points

Let $x$ = years after 2016, $y$ = height (ft).
Points: $(0, 7.5)$ (2016), $(6, 21)$ (2022, 2022-2016=6)

Step2: Calculate growth rate (slope)

Slope $m = \frac{21 - 7.5}{6 - 0} = \frac{13.5}{6} = 2.25$

Step3: Identify y-intercept

When $x=0$, $y=7.5$, so $b=7.5$.

Step4: Write linear equation

Use $y=mx+b$: $y=2.25x+7.5$

Answer:

$y = 2.25x + 7.5$