Question

mr. ford wants to better understand the value of used cars over time. he reviewed some used - car ads and recorded the relationship between age and price in a table. finally, he calculated a line of best fit.

used cars
price (y)	$15,000	$8,000	$12,000	$5,000	$19,000	$10,000

the equation for the line of best fit is $y = - 2,200x + 22,000$.
based on the equation, what estimates can you make about the used cars mr. ford reviewed? select all that apply.

• these used cars are worth roughly $2,200 less now than when they were new.
• these used cars likely had an average price around $22,000 when new.
• these used cars typically lose $2,200 of value per year.
• at 5 years old, these used cars had an average value of around $11,000.

Explanation:

Step1: Analyze the y-intercept

The y-intercept (when \(x=0\), age=0) is 22,000, so new cars average ~$22k.

Step2: Analyze the slope

The slope is -2200, meaning value decreases by $2200 per year.

Step3: Calculate price at x=5

Substitute \(x=5\) into \(y=-2200x + 22000\):
\(y=-2200(5)+22000=-11000+22000=11000\), so ~$11k at 5 years.

Step4: Evaluate first option

The first option says "worth roughly $2200 less now than new"—this is incorrect because the decrease depends on age, not a fixed $2200 from new. The slope is per year, not total from new.

Answer:

These used cars likely had an average price around $22,000 when new.
These used cars typically lose $2,200 of value per year.
At 5 years old, these used cars had an average value of around $11,000.