Question

The expected number y (in millions) of employed registered nurses x years after 2012 is given by the equation y=0.83x +2.71.a) Find the slope of this equation. Explain what this slope signifies.b) Find the y-intercept of the equation. Explain what this y-intercept signifies.c) Use the equation to predict the number of employed registered nurses 2027.(Type integers or decimals.)OA. The slope of the equation is which signifies that in 2012 there were approximately million employed registered nurses.B. The slope of the equation is which signifies that each year the number of employed registered nurses will increase byOC. The slope of the equation is, which signifies that each year the number of employed registered nurses will decrease byb) Select the correct choice below and fill in the answer boxes to complete your choice.(Type an ordered pair. Type an integer or a decimal.)A. The y-intercept isB. The y-intercept isC. The y-intercept isc) The predicted number of employed registered nurses in 2027 is million.which signifies that each year the number of employed registered nurses will decrease bywhich signifies that each year the number of employed registered nurses will increase bywhich signifies that in 2012 there were approximately million employed registered nurses.million.million.million.million.

Answer 1

Given: The equation relating the expected number of employed registered nurses and the number of years after 2012 is

`y=0.83x+2.71`

To Determine: The slope

Solution

Given the general equation of a line in slope-intercept form

`\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}`

Let us compare the given equation to the general equation of a line in slope-intercept form as shown above

`\begin{gathered} y=mx+c \\ y=0.83x+2.71 \\ slope=m=0.83 \\ y-intercept=c=2.71 \end{gathered}`

The total number of years from 2012 to 2027 is

`\begin{gathered} x=2027-2012 \\ x=15 \end{gathered}`
`\begin{gathered} y=0.83x+2.71 \\ y=0.83(15)+2.71 \\ y=12.45+2.71 \\ y=15.16 \end{gathered}`

Hence:

(a) The slope is 0.83, which signifies that each year the number of employed registered nurses will increase by 0.83 million, OPTION B

(b) The y-intercept is 2.71, which signifies that in 2012 there were approximately 2.71 million employed registered nurses, OPTION C

(c) The predicted number of employed number of registered nurses in 2027 is 15.16 million