Question

interpret linear function coefficients (from equation)
score: 0/3 penalty: none
question
sarah accepted a new job at a company with a contract guaranteeing annual raises. sarahs salary after working for n years can be determined using the equation s = 90000 + 3500n. what is the slope of the equation and what is its interpretation in the context of the problem?
answer attempt 1 out of 5
the slope of the function is
which represents
sarahs salary when hired
the number of years sarah must work for the company
the salary in sarahs nth year of working
the raise that sarah will get each year

Explanation:

Step1: Recall slope-intercept form

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 given equation \(S=90000 + 3500n\), we can rewrite it as \(S = 3500n+90000\), which is in the form of \(y=mx + b\) (here \(y = S\), \(x = n\), \(m\) is the slope and \(b\) is the y - intercept).

Step2: Identify the slope

Comparing \(S = 3500n+90000\) with \(y = mx + b\), we can see that the coefficient of \(n\) (the independent variable) is the slope. So the slope \(m = 3500\).

Step3: Interpret the slope

The slope represents the rate of change of the dependent variable (salary \(S\)) with respect to the independent variable (number of years \(n\)). Since the slope is 3500, it means that for each additional year (\(n\) increases by 1), Sarah's salary (\(S\)) increases by 3500. So the slope represents the raise that Sarah will get each year.

Answer:

The slope of the function is \(3500\) which represents the raise that Sarah will get each year.