Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 2a – Linear Functions and Applications
Mini-Lesson
Given Input, Find Output and Given Output, Find Input Questions
When working with LINEAR FUNCTIONS, there are two main questions we will ask and solve
as follows:
Given a particular INPUT value, what is the corresponding OUTPUT value? To address
this question, you will EVALUTE the function at the given input by replacing the input
variable with the input value and computing the result.
Given a particular OUTPUT value, what is the corresponding INPUT value? To address
this question, you will set the equation equal to the output value and solve for the value of
the input.
Problem 4 YOU TRY – APPLICATIONS OF LINEAR FUNCTIONS
The data below represent your annual salary for the first four years of your current job. The data
are exactly linear.
Time, t, in years 0 1 2 3 4
Salary, S, in $ 20,100 20,600 21,100 21,600 22,100
a) Identify the vertical intercept and average rate of change for the data, then use these to write
the linear function model for the data. Use the indicated variables and proper function
notation.
b) Use your model to determine the amount of your salary in year 8. [Note: This is a “Given
Input, Find Output” question.] Write your final result as a complete sentence.
c) Use your model to determine how many years you would need to work to earn a yearly
salary of at least $40,000. Round to the nearest whole year. [Note: This is a “Given Output,
Find Input” question.]. Write your final result as a complete sentence.
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