Question

select all the correct answers.

brendon is walking home from a place that is 1.5 miles away. the function \\(y = 7,920 - 270x\\) represents brendons distance in feet from home, \\(y\\), in relation to the number of minutes he walks, \\(x\\). bryan is also walking home. every 15 minutes, he writes down the number of feet left to reach home, as shown in the table.

\

$$\begin{array}{|c|c|} \\hline \\text{minutes} & \\text{feet} \\\\ \\hline 0 & 8,000 \\\\ \\hline 15 & 3,800 \\\\ \\hline \\end{array}$$

which statements about this situation are true?

• brendon walks faster.
• bryan walks faster.
• brendon and bryan walk at the same speed.
• brendon was farther away from home when he started walking.
• bryan was farther away from home when he started walking.
• brendon and bryan were an equal distance from home when they started walking.

Explanation:

Analyze Brendon's walking parameters

Using the Linear Equation Modeling knowledge point

$$ y = 7920 - 270x $$

• Initial distance (\(x = 0\)): \(7,920\text{ feet}\)
• Speed (rate of change): \(270\text{ feet per minute}\)

Analyze Bryan's walking parameters

Using the Rate of Change knowledge point

• Initial distance (\(x = 0\)): \(8,000\text{ feet}\)
• Distance at \(x = 15\): \(3,800\text{ feet}\)
• Speed calculation:

$$ \text{Speed} = \frac{8000 - 3800}{15} = \frac{4200}{15} = 280\text{ feet per minute} $$

Compare speeds and starting distances

• Speed comparison: Bryan (\(280\text{ ft/min}\)) walks faster than Brendon (\(270\text{ ft/min}\)).
• Starting distance comparison: Bryan (\(8,000\text{ feet}\)) was farther from home than Brendon (\(7,920\text{ feet}\)).

Answer:

• Brendon walks faster.
• Bryan walks faster. (Correct answer)
• Brendon and Bryan walk at the same speed.
• Brendon was farther away from home when he started walking.
• Bryan was farther away from home when he started walking. (Correct answer)
• Brendon and Bryan were an equal distance from home when they started walking.