# Study Guide 5.1 ```Section 5.1 Study Guide
Linear Functions
Linear functions are quantities that have a constant rate of increase (or decrease).
Example 1
The school-age population, P of a school district begins at 1000 children and increases at a constant rate
of 50 students per year.
a)
Write a formula for this population:____________________________________________
b)
Fill in the table based on your formula:
t
0
10
20
30
40
50
P
c)
Graph the values on the graph below. Decide as a group if you should connect the points or not.
d)
Find the rate of change for the function between:
i.
t= 10 and t=20
ii.
e)
t=30 and t=50
How do these rates of change relate to the formula? What about the graph?
Based on these results, in the following equation: f(t) = b + mt,
m represents: ______________________________ or _____________________________
b represents:_______________________________ or ______________________________
Example 2
For the function g(x) = 8 – 3x
a)
What does the coefficient of x tell you about the graph?
b)
What is the vertical intercept (y-intercept)?
c)
Use this information to graph the function.
Example 3
The population of a town grew at a constant rate from 25,000 people in 1995 to 45,000 people in 2005.
a)
Find a linear function for the population, P, t years after 1995.
b)
Give the units and practical interpretation of the slope and vertical intercept.
Work through problem 34 from p 121 below.
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