Question

select the correct answer from each drop-down menu.
andrew planted a tree and joseph planted a seed in their backyard. the growth of andrew’s tree is represented by the graph shown.
tree growth over years
joseph’s seed became a tree that grew 17 feet every 2 years since it was planted. graph the growth of the tree joseph planted. then, determine how many years it takes for the two trees to be the same height. round to the nearest whole number.
approximately years after joseph tree was planted, both trees will be the same height of approximately feet.

Explanation:

Step1: Find Andrew's tree equation

From graph: at $x=0$, $y=15$ (intercept $b=15$). Slope $m=\frac{45-15}{6-0}=5$. So $y=5x+15$.

Step2: Find Joseph's tree equation

Rate: $\frac{17}{2}=8.5$ ft/year. Equation: $y=8.5x$.

Step3: Set equations equal

$8.5x = 5x + 15$

Step4: Solve for x

$3.5x=15 \Rightarrow x=\frac{15}{3.5}\approx4.2857$? Correction: Wait, Andrew's tree: check graph again—at $x=10$, $y=55$? No, original graph: $x=0$ (15ft), $x=2$ (25ft), slope=5. Joseph: 17ft/2yrs=8.5ft/yr. Set $5x+15=8.5x \Rightarrow 3.5x=15 \Rightarrow x≈4.2857$? No, wait—wait, maybe Andrew's tree age vs Joseph's: if Andrew's tree was already 15ft when Joseph planted? No, problem says "since it was planted" for both. Wait correction: Andrew's tree: let’s take two points: (0,15) and (10,65)? No, the correct intersection: $5x+15=8.5x \Rightarrow x≈4.2857$ is wrong. Wait no—wait 17ft every 2 years: so per year 8.5. Andrew’s slope: from graph, 15ft at 0, 25ft at 2: slope=5. So $5x+15=8.5x \Rightarrow x=15/3.5≈4.2857$? But the problem says "round to nearest whole number"—wait maybe I misread the graph: if Andrew’s tree at x=10 is 65? No, let's do exact: $x=15/3.5≈4.2857≈4$ years? But wait, 4 years: Andrew’s height=54+15=35, Joseph’s=8.54=34≈35. Yes! So 4 years, 34≈35 feet.

Wait correction final:

Step1: Andrew's line: $y=5x+15$

Step2: Joseph's line: $y=8.5x$

Step3: Intersection: $8.5x=5x+15 \Rightarrow x≈4.29≈4$ years, height≈8.5*4=34≈35 feet.

Step1: Andrew's tree formula

$y = 5x + 15$ (slope=5, intercept=15)

Step2: Joseph's tree formula

$y = 8.5x$ (rate=8.5 ft/year)

Step3: Solve for equal height

$8.5x = 5x + 15 \Rightarrow 3.5x=15 \Rightarrow x≈4.29$

Step4: Round and find height

$x≈4$ years, height≈8.5*4=34≈35 feet.

Final Answer: 4, 35

Answer:

10 years, 85 feet