SOLUTION: Bob is hired by an accounting firm at a salary of $60,000 per year. Three years later his annual salary has increased to $70,500. Assume his salary increases linearly. 1. Find a

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Question 511508: Bob is hired by an accounting firm at a salary of $60,000 per year. Three years later his annual salary has increased to $70,500. Assume his salary increases linearly.
1. Find an equation that relates his annual salary...S and the number of years...t that he has worked for the firm.
2. What do the slope and the S-intercept of his salary equation represent?
3. What will his salary be after 12 years with the firm?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Think of an x-y plot where x is the years passed
and y is the salary
I can say when
+S+=+60+ ( salary in thousands)
+t+=+0+
---------
when
+S+=+70.5+
+t+=+3+
---------
I can write the equation in point-slope form
+%28+S+-+60+%29+%2F+%28+t+-+0+%29+=+%2870.5+-+60+%29+%2F+%283+-+0+%29+
+%28+S+-+60+%29+%2F+t+=+10.5+%2F+3+
multiply both sides by +3t+
+3%2A%28+S+-+60+%29+=+10.5t+
+3S+-+180+=+10.5t+
+3S+=+10.5t+%2B+180+
+S+=+3.5t+%2B+60+
check:
When +t=0+, he makes $60 thousand -OK
When +t+=+3+, he makes +3.5%2A3+%2B+60+=+70.5+ thousand -OK
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The slope is how fast his salary is increasing
The S-intercept is his starting salary
--------------
After 12 years,
+S+=+3.5%2A12+%2B+60+
+S+=+42+%2B+60+
+S+=+102+
He will make $102,000 after 12 years