Question

employee salaries
the equation for the line of best fit is ( y = 1,360x + 29,830 ). according to the equation,
which of these statements about the department store is true?
a salespersons annual salary can be expected to increase by about ( $29,830 )
for each additional year of employment.
a salespersons annual salary can be expected to increase by about ( $1,360 )
for each additional year of employment.

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(y=1360x + 29830\), \(x\) represents the number of years of employment and \(y\) represents the annual salary.

Step2: Interpret the slope

The slope \(m = 1360\). In the context of the problem, the slope represents the rate of change of \(y\) (annual salary) with respect to \(x\) (years of employment). Mathematically, \(\text{Rate of change}=\frac{\Delta y}{\Delta x}\). When \(\Delta x = 1\) (one additional year of employment), \(\Delta y=m\times\Delta x\). Substituting \(\Delta x = 1\) and \(m = 1360\), we get \(\Delta y=1360\times1 = 1360\). This means that for each additional year of employment (\(x\) increases by 1), the annual salary (\(y\)) increases by \(1360\).

Answer:

A salesperson’s annual salary can be expected to increase by about \(\$1,360\) for each additional year of employment.