Question

a person earns a starting salary of $16 thousand at a company. each year, she receives a $2 thousand raise. let s be the salary (thousands of dollars) after she has worked at the company for t years. complete parts (a) through (e).
d. what is the s-intercept? what does it mean in this situation?
select the correct choice and fill in the answer box to complete your choice.
(type an ordered pair.)
○ a. the s-intercept of the model is, and it represents the persons salary when she quits the job.
○ b. the s-intercept of the model is, and it represents the persons salary when she joined the company.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $s = mt + b$, where $m$ is the slope and $b$ is the $s$ - intercept (the value of $s$ when $t = 0$).
In this situation, the starting salary (when $t = 0$, i.e., when she has worked for 0 years) is $16$ thousand dollars. The rate of change of salary per year (the slope $m$) is $2$ thousand dollars per year. So the equation of the salary function is $s=2t + 16$.

Step2: Find the $s$ - intercept

To find the $s$ - intercept, we set $t = 0$ in the equation $s = 2t+16$. When $t = 0$, $s=2(0)+16 = 16$. In terms of an ordered pair $(t,s)$, when $t = 0$, $s = 16$, so the $s$ - intercept is the point $(0,16)$.

Step3: Interpret the $s$ - intercept

When $t = 0$, it means the time when she has worked at the company for 0 years, which is the time when she joined the company. So the $s$ - intercept represents her salary when she joined the company. So option B is correct.

Answer:

B. The s - intercept of the model is $\boldsymbol{(0,16)}$, and it represents the person's salary when she joined the company.