Question

dylan accepted a new job at a company with a contract guaranteeing annual raises. let s represent dylan’s salary after working for n years at the company. the table below has select values showing the linear relationship between n and s. determine dylan’s salary when hired.

n	2	5	8
s	93000	105000	117000

Explanation:

Step1: Find the slope (rate of change)

The slope \( m \) of a line passing through two points \((n_1, S_1)\) and \((n_2, S_2)\) is given by \( m=\frac{S_2 - S_1}{n_2 - n_1} \). Let's take the points \((2, 93000)\) and \((5, 105000)\).
\( m=\frac{105000 - 93000}{5 - 2}=\frac{12000}{3} = 4000 \)

Step2: Use point - slope form to find the equation of the line

The point - slope form of a line is \( S - S_1=m(n - n_1) \). Using the point \((2, 93000)\) and \( m = 4000 \):
\( S-93000 = 4000(n - 2) \)
Expand the right - hand side: \( S-93000=4000n-8000 \)
Then, solve for \( S \): \( S = 4000n-8000 + 93000=4000n + 85000 \)

Step3: Find the salary when hired (n = 0)

When Dylan is hired, \( n = 0 \). Substitute \( n = 0 \) into the equation \( S = 4000n+85000 \):
\( S=4000(0)+85000=85000 \)

Answer:

85000