Identifying Linear Functions
Objective: I CAN . . . Identify and graph linear functions and linear equations.
REMEMBER: A graph represents a function if it passes the _________________________ test.
A ____________________ function forms a straight line when graphed,
Identify whether each graph represents a function. If the graph does represent a function, is the function linear?
C.
Function:
Yes
or No
Yes
or No
Yes
or No
Linear:
Yes
or No
Yes
or No
Yes
or No
D.
E.
F.
Function:
Yes
or No
Yes
or No
Yes
or No
Linear:
Yes
or No
Yes
or No
Yes
or No
o In a linear function, a constant change in x corresponds to a constant change in y.
Are the following tables linear?
a.
b.
c.
{(3, 5), (5, 4), (7, 3), (9, 2), (11, 1)}
d.
{(–4, 13), (–2, 1), (0, –3), (2, 1), (4, 13)}
Circle the function that is linear.
a. x = 2y + 4
b. xy = 4
c. 12x + y = 5x – 9
e. y = 2x
d. y = 12
Tell whether the function is linear. If so, graph the function.
a. y  5x  9
X
3x  y  4
b.
(x,y)
X
(x,y)
Intercepts
Objective: I CAN . . . Use intercepts to graph lines.
Find intercepts and interpret their meanings in real world situations.
Steps to Find Intercepts:
1. Find the x and y intercepts.
2. Plot the two points and draw the line.
a. To find the x-int. : _______________________________________________
b. To find the y-int. : _______________________________________________
(
(
,
)
,
)
Ex. 1: Graphing Using Intercepts:
a) 5x + 3y = 15
c)
1
x  8y  4
2
b) -2x + 5y = 10
d)
4 x  3 y  24
1. A car owner recorded the number of gallons of gas remaining in the car's gas tank after driving a number of miles.
Use the graph below to answer the following questions.
a. What does x-intercept represent on the graph?
b. What does the y-intercept represent on the graph?
c. What does the point (200, 12) represent on the graph? Is the
point a solution of the graph?
d. What does the point (400, 10) represent on the graph?
Is the point a solution of the graph?
2. The graph below shows the relationship between the number of mid-sized cars in a car dealer's inventory and the
number of days after the start of a sale.
a. What does x-intercept represent on the graph?
b. What does the y-intercept represent on the graph?
c. What does the point (10, 50) represent on the graph?
Is the point a solution of the graph?
d.
What does the point (5, 125) represent on the graph?
Is the point a solution of the graph?
Rate of Change/Slope
Objective: I CAN. . . Find the slope of a line and rate of change.
Slope - is the _________________ of the line
_____________ Slope
____________ Slope
____________ Slope
_______________ Slope
Find the slope using the graph: m 
1.
4.
2.
3.
5.
6.
Rate of Change = Slope
Applications:
7.
The graph shows the altitude of a plane.
a. Find the plane’s rate of change during the first hour.
b. Find the plane’s rate of change during the second hour.
8.
An industrial-safety study finds there is a relationship between the number of industrial accidents and the
number of hours of safety training for employees. This relationship is shown in the graph below.
a.
Find the rate of change.
b.
Explain what it represents.
The Slope Formula
Objective: I CAN . . . Find the slope by using the slope formula.
Slope between two points on a line:
m
( x1 , y1 ) ( x2 , y2 )
y1  y2
x1  x2

changein y
changein x
Find the slope of the line that contains the two points.
1.
3,5 & 1, 4
2.
 2,1 & 1, 3
Find the slope of the line from a given graph.
3.
1, 2 & 5, 2
4.
5, 1 & 5,3
*** Remember to find slope of a graph: m 
5.
6. The table shows a linear relationship. Find the slope.
7. In 2005, Joe planted a tree that was 3 feet tall. In 2010, it was 13 feet tall.
a) Find the rate of change.
b) How tall would you predict it would be now in 2013?
c) How tall you do you predict it will be 50 years?