Question

a scatter plot was made to show the value of certain cars based on the age of the car in years. the equation of the scatter plot’s trend line is y = -1,700x + 32,000 where y is the value of the car in dollars, and x is the number of years since it’s been bought. what is the slope of the line of best fit? what does the slope mean in context? correct! the value of the car decreases by $1,700 per 1 year the value of the car increases by $1 per 1,700 years the value of the car decreases by $1 every 1,700 years

Explanation:

Step1: Recall the slope - intercept form of a line

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Identify the slope from the given equation

Given the equation \(y=-1700x + 32000\), comparing it with \(y = mx + b\), we can see that \(m=-1700\).

Step3: Interpret the slope in context

The slope \(m=-1700\) means that for each unit increase in \(x\) (where \(x\) is the age of the car in years), the value of \(y\) (the value of the car in dollars) changes. Since \(x\) represents the number of years since the car was bought, when \(x\) increases by 1 (one more year), \(y\) (the value of the car) decreases by 1700.

Answer:

The slope of the line of best fit is \(-1700\), and it means the value of the car decreases by \(\$1700\) per 1 year.