Question

the table below shows the cost of health care, in millions of dollars, from 1996 to 2001. cost of health care the equation of a line of best fit for this data is ( y = 30x + 474 ), where ( x ) represents the number of years since 1996 and ( y ) represents the cost of health care, in millions of dollars. which statement best describes the meaning of the slope of this equation? the cost of health care increased by $30,000,000 per year since 1996. the cost of health care increased by $30 per year since 1996. the cost of health care increased by $474 per year since 1996. the cost of health care increased by $474,000,000 per year since 1996.

Explanation:

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

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the equation \(y = 30x+474\), \(x\) represents the number of years since 1996 and \(y\) represents the cost of health care in millions of dollars.

Step2: Analyze the meaning of the slope

The slope \(m = 30\). Since \(y\) is in millions of dollars and \(x\) is the number of years. The slope \(m=\frac{\Delta y}{\Delta x}\), which means for each increase of \(x\) (one year), \(y\) (the cost of health care in millions of dollars) increases by 30. So the cost of health care increases by \(30\times1000000=\$30000000\) per year.

Answer:

The cost of health care increased by \(\$30,000,000\) per year since 1996.