1. A family of functions is a group of functions
with similar characteristics. For example,
functions in the form of f(x) = mx + b
constitutes the family of linear functions.
f(x) = x
Is called the
parent linear
function.
y=x

2. EXAMPLE 4 Compare graphs with the graph f (x) = x
Graph the function. Compare the graph with the graph
of f (x) = x.
g(x) = x + 3
SOLUTION
Because the graphs of g and
f have the same slope, m = 1,
the lines are parallel. Also,
the y- intercept of the graph
of g is 3 more than the y-
intercept of the graph of f.

3. EXAMPLE 4 Compare graphs with the graph f (x) = x
h(x) = 2x
SOLUTION Because the slope of the graph of
h is greater than the slope of
the graph of f, the graph of h
rises faster from left to right.
The y-intercept for both
graphs is 0, so both lines pass
through the origin.

4. GUIDED PRACTICE an equation from a graph
Write
Graph h(x) = – 3x. Compare the graph with the
graph of f (x) = x.
SOLUTION
Since the slope of the graph of
h is negative the graph of h falls
from left to right. The y-
intercept for both graphs is 0,
so both lines pass through the
origin.

5. What is the linear function that matches
this graph? Compare it to f(x) = x

6.  Assignment: Cont’ P. 266 (#23-26, 29-
31, 39-41)

7. Big Ideas for the Quiz
 Find the slope – given two points
 Find the slope – given a graph
 Tell if an equation represents “direct
variation” – if so, give the constant of
variation.
 Given an equation, find the slope and y-
intercept.
 Decide if two functions / equations are
parallel (without graphing)

8.  Re-write an equation in slope-intercept
from
 Word problem – graph and compare
 Given an equation, write another
equation that will parallel to that one.