Question

A teacher in Colorado receives an annual salary increase of $1,500 each year they continue to work at a school within a district. If Mr. Brown has an initial salary of $40,000, using the function s=1,500y+40,000
, where s is the total salary and y is the time in years, which of the following points on the graph represent how much Mr. Brown will make for teaching 3, 4, and 5 years in the district?

a. (3, 4, 500), (4, 6, 000), and (5, 7, 500)
b. (-3, 44, 500), (-4, 46, 000), and (5, 7, 500)
c. (44, 500, 3), (46, 000, 4), and (-5, 47, 500)
d. (3, 44, 500), (4, 46, 000), and (5, 47, 500)

Answer 1

To find Mr. Brown's salary after teaching for 3, 4, and 5 years, we can use the given function:

\[ s = 1,500y + 40,000 \]

where \( s \) is the total salary and \( y \) is the number of years.

Now, let's calculate the salary for each of those years:

1. **For 3 years (y = 3):**
\[
s = 1,500(3) + 40,000 = 4,500 + 40,000 = 44,500
\]
So, after 3 years, Mr. Brown will earn $44,500.

2. **For 4 years (y = 4):**
\[
s = 1,500(4) + 40,000 = 6,000 + 40,000 = 46,000
\]
Thus, after 4 years, Mr. Brown will earn $46,000.

3. **For 5 years (y = 5):**
\[
s = 1,500(5) + 40,000 = 7,500 + 40,000 = 47,500
\]
Therefore, after 5 years, Mr. Brown will earn $47,500.

Now that we have the computed salaries:

- For 3 years: (3, 44,500)
- For 4 years: (4, 46,000)
- For 5 years: (5, 47,500)

Looking at the options provided:

- **Option a**: (3, 44,500), (4, 46,000), and (5, 7,500) [Incorrect; the salary for 5 years is wrong]
- **Option b**: (-3, 44,500), (-4, 46,000), and (5, 7,500) [Incorrect; negative years are not valid]
- **Option c**: (44,500, 3), (46,000, 4), and (-5, 47,500) [Incorrect; the values are not correctly paired]
- **Option d**: (3, 44,500), (4, 46,000), and (5, 47,500) [Correct]

Therefore, the correct answer is **d**: (3, 44,500), (4, 46,000), and (5, 47,500).