Question

One of the top 10 occupations in terms of job growth in the next few years is expected to be registered nurses. The number of​ people, y, in​ thousands, employed as registered nurses in a certain country can be estimated by the linear equation

559 x minus 10 y equals negative 27 comma 010
559x−10y=−27,010​, where x is the number of years after 2012.
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?

Answer 1

Answer: a. To find the slope and y-intercept of the linear equation, we need to write it in slope-intercept form (y = mx + b). To do this, we can add 10y to both sides and divide both sides by 10 to get:

y = -559x/10 - 2701/10

y = -55.9x - 270.1

The slope of the equation is -55.9, and the y-intercept is -270.1

b. The slope of a linear equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this context, the slope of -55.9 means that for every year after 2012, the number of people employed as registered nurses is expected to decrease by 55.9 thousand.

c. The y-intercept of a linear equation is the point where the line crosses the y-axis. In this context, the y-intercept of -270.1 means that in 2012, there were expected to be 270.1 thousand people employed as registered nurses.

Explanation: