Question

the equation for the line of best fit is ( y = 0.5x + 12 ). according to the equation, which of these statements is true? on average, an employees hourly wage increases by about $12 each year. a new employee should expect to earn about $12 per hour.

Explanation:

Step1: Analyze the slope - intercept form of the 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 \(y = 0.5x+12\), \(m = 0.5\) and \(b = 12\).

Step2: Interpret the slope and \(y\) - intercept

The slope \(m = 0.5\) represents the rate of change. For each unit increase in \(x\) (years of employment), \(y\) (hourly wage) increases by \(m\). So, the hourly wage increases by about \(\$0.5\) per year. The \(y\) - intercept \(b = 12\) is the value of \(y\) when \(x = 0\). When \(x = 0\) (new employee, 0 years of employment), \(y=0.5\times0 + 12=12\).

Answer:

A new employee should expect to earn about \(\$12\) per hour.