Question

one of the occupations expected to have the most employment growth between 2019 and 2029 is registered nurses. the number of people, y (in thousands) employed as registered nurses in a certain country can be estimated by the equation 24.4x - 10y = -30,900, where x is the number of years after 2019.
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?
the y-intercept is (0,3090) (type an ordered pair. use integers or decimals for any numbers in the expression. do not use commas in the individual coordinates.)
there is no y-intercept.
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. the number of people employed as registered nurses increases for every 1 year.
c. there were thousand registered nurses employed in 2019.
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 2019.

Explanation:

Part a: Find the slope and the y - intercept of the linear equation \(244x - 10y=- 30900\)

Step 1: Rewrite the equation in slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept)

Start with the given equation \(244x-10y=-30900\).
First, isolate \(y\). Subtract \(244x\) from both sides:
\(- 10y=-244x - 30900\)
Then, divide each term by \(- 10\):
\(y=\frac{-244x}{-10}+\frac{-30900}{-10}\)
Simplify the fractions:
\(y = 24.4x+3090\)

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 \(b = 3090\). The y - intercept as an ordered pair is \((0,3090)\) (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 per year). In the context of the number of registered nurses employed, 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 \(x\) is the number of years after 2019, when \(x = 0\), it represents the year 2019. And \(y\) is the number of people (in thousands) employed as registered nurses. So the y - intercept (\(y = 3090\) when \(x = 0\)) means there were \(3090\) thousand registered nurses employed in 2019. So the correct option is C.

Final Answers:

a. Slope: \(24.4\), y - intercept: \((0,3090)\)
b. \(\boldsymbol{\text{A}}\)
c. \(\boldsymbol{\text{C}}\)

Answer:

Part a: Find the slope and the y - intercept of the linear equation \(244x - 10y=- 30900\)

Step 1: Rewrite the equation in slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept)

Start with the given equation \(244x-10y=-30900\).
First, isolate \(y\). Subtract \(244x\) from both sides:
\(- 10y=-244x - 30900\)
Then, divide each term by \(- 10\):
\(y=\frac{-244x}{-10}+\frac{-30900}{-10}\)
Simplify the fractions:
\(y = 24.4x+3090\)

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 \(b = 3090\). The y - intercept as an ordered pair is \((0,3090)\) (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 per year). In the context of the number of registered nurses employed, 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 \(x\) is the number of years after 2019, when \(x = 0\), it represents the year 2019. And \(y\) is the number of people (in thousands) employed as registered nurses. So the y - intercept (\(y = 3090\) when \(x = 0\)) means there were \(3090\) thousand registered nurses employed in 2019. So the correct option is C.

Final Answers:

a. Slope: \(24.4\), y - intercept: \((0,3090)\)
b. \(\boldsymbol{\text{A}}\)
c. \(\boldsymbol{\text{C}}\)