Question

one of the occupations expected to have the most employment growth between 2010 and 2020 is registered nurses. the number of people, y (in thousands) employed as registered nurses in a certain county can be estimated by the linear equation 244x − 10y = −30,590, where x is the number of years after 2010.
a. find the slope and the y-intercept of the linear equation.
b. what does the slope mean in this context?
c. what does the y-intercept mean in this context?
(then parts: a. the y-intercept is (0, 3059) (type an ordered pair. use integers or decimals for any numbers in the expression. do not use commas in the individual coordinates)
b. select the correct choice below and fill in the answer box to complete your choice. (type an integer or a decimal)
a. the number of people employed as registered nurses increases 24.4 thousand for every 1 year.
b. there were thousand registered nurses employed in 2016.
c. the number of people employed as registered nurses increases 1 thousand for every years.
c. select the correct choice below and fill in the answer box to complete your choice.
a. the number of people employed as registered nurses increases 1 thousand for every years.
b. the number of people employed as registered nurses increases for every 1 year.
c. there were registered nurses employed in 2010.)

Explanation:

Part a: Find the slope and the y - intercept of the linear equation

The given equation is \(244x-10y=- 30550\). We can rewrite it in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step 1: Solve the equation for \(y\)

Start with \(244x-10y=-30550\).
Subtract \(244x\) from both sides: \(- 10y=-244x - 30550\).
Divide each term by \(- 10\): \(y=\frac{-244x}{-10}+\frac{-30550}{-10}\).
Simplify the fractions: \(y = 24.4x+3055\).

Step 2: Identify the slope and y - intercept

In the slope - intercept form \(y=mx + b\), the coefficient of \(x\) (\(m\)) is the slope and the constant term (\(b\)) is the y - intercept.
So, the slope \(m = 24.4\) and the y - intercept \(b = 3055\). The y - intercept as an ordered pair is \((0,3055)\) (since when \(x = 0\), \(y=b\)).

Part b: What does the slope mean in this context?

The slope \(m = 24.4\) (in thousands of people). Since \(y\) is the number of people (in thousands) employed as registered nurses and \(x\) is the number of years after 2010, the slope means that the number of people employed as registered nurses increases by \(24.4\) thousand for every 1 year. So the correct option is A.

Part c: What does the y - intercept mean in this context?

The y - intercept is the value of \(y\) when \(x = 0\). Since \(x = 0\) represents the year 2010 (because \(x\) is the number of years after 2010), the y - intercept \(y = 3055\) (in thousands) means that there were \(3055\) thousand registered nurses employed in 2010. So the correct option is C.

Final Answers

a. The slope is \(24.4\) and the y - intercept is \((0,3055)\)
b. The answer is A. The number of people employed as registered nurses increases \(24.4\) thousand for every 1 year.
c. The answer is C. There were \(3055\) thousand registered nurses employed in 2010.

Answer:

Part a: Find the slope and the y - intercept of the linear equation

The given equation is \(244x-10y=- 30550\). We can rewrite it in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step 1: Solve the equation for \(y\)

Start with \(244x-10y=-30550\).
Subtract \(244x\) from both sides: \(- 10y=-244x - 30550\).
Divide each term by \(- 10\): \(y=\frac{-244x}{-10}+\frac{-30550}{-10}\).
Simplify the fractions: \(y = 24.4x+3055\).

Step 2: Identify the slope and y - intercept

In the slope - intercept form \(y=mx + b\), the coefficient of \(x\) (\(m\)) is the slope and the constant term (\(b\)) is the y - intercept.
So, the slope \(m = 24.4\) and the y - intercept \(b = 3055\). The y - intercept as an ordered pair is \((0,3055)\) (since when \(x = 0\), \(y=b\)).

Part b: What does the slope mean in this context?

The slope \(m = 24.4\) (in thousands of people). Since \(y\) is the number of people (in thousands) employed as registered nurses and \(x\) is the number of years after 2010, the slope means that the number of people employed as registered nurses increases by \(24.4\) thousand for every 1 year. So the correct option is A.

Part c: What does the y - intercept mean in this context?

The y - intercept is the value of \(y\) when \(x = 0\). Since \(x = 0\) represents the year 2010 (because \(x\) is the number of years after 2010), the y - intercept \(y = 3055\) (in thousands) means that there were \(3055\) thousand registered nurses employed in 2010. So the correct option is C.

Final Answers

a. The slope is \(24.4\) and the y - intercept is \((0,3055)\)
b. The answer is A. The number of people employed as registered nurses increases \(24.4\) thousand for every 1 year.
c. The answer is C. There were \(3055\) thousand registered nurses employed in 2010.