Name:__________________________
Linear Functions Unit Review
REMEMBER: A graph represents a function if it passes the _________________________ test.
A ____________________ function forms a straight line when graphed.
What are the 5 ways to represent relations and/or functions?
Tell 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.
o
c.
{(3, 5), (5, 4), (7, 3), (9, 2), (11, 1)}
d.
{(–4, 13), (–2, 1), (0, –3), (2, 1), (4, 13)}
For linear equation, both x and y have an exponent of 1
Ex. __________________

x and y do not have exponent other than 1
Non-Ex. ______________

x and y are not multiplied together
Non-Ex. ______________

x and y are not in denominators,
Non-Ex. ______________

x and y are not exponents
Non-Ex. ______________

x and y do not include radicals
Non-Ex. ______________
Circle the function(s) that are linear.
a. x = 2y + 4
b. xy = 4
c. 12x + y = 5x – 9
d. y = 12
Tell whether the function is linear. If so, graph the function.
a. y  5x  9
X
b.
Y
3x  y  4
X
Y
e. y = 2x
Rewrite the following into slope-intercept form. Then graph the equations.
a) 5x + 3y = 15
c)
b) -2x + 5y = 10
1
x  8y  4
2
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 the point (500, 0) represent in the context of the graph?
b. What does the y-intercept represent in the context of the graph?
c. What does the point (200, 12) represent on the graph? Is the
point a solution on the graph?
d. What does the point (400, 10) represent on the graph? Is the point a
solution on 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. Write an equation to model this situation.
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?
Slope - is the _________________ of the line
_____________ Slope
____________ Slope
____________ Slope
_______________ Slope
Find the slope using the graph: m 
1.
2.
3.
4.
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.
 If the slope of a line is changed it will either become ____________________ or ______________________.
 If the y-intercept of a line is changed it will either be ____________________ or ______________________.
Describe how the original line is affected with the changes.
1. y  3 x  2 is changed if the slope is changed to
1
.
3
Revised Equation:________________
Describe Affects:_______________________________
2. y  2 x  3 is changed if the y-intercept is changed to 6.
Revised Equation:________________
Describe Affects:_______________________________
3. y 
1
2
x  2 is changed if the slope is changed to .
3
2
Revised Equation:________________
Describe Affects:_______________________________
3
4
4. y   x  6 is changed if the y-intercept is changed to 4 .
Revised Equation:________________
Describe Affects:_______________________________
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?
Name__________________________________
Date___________________
T-Shirts for the Walkathon
Mr. Macedo has decided to give t-shirts to each student who participates in the
walkathon. He received bids for the cost of t-shirts from two different
companies. The Mighty-Tee Company charges $24 for the set-up plus $2 per tshirt. The No-Shrink Tee Company charges $5 per t-shirt.
1. Complete the table to show the cost for 0 to 10 t-shirts for each company.
2. Write an equation to represent the cost for each t-shirt company.
a. Mighty-Tee Company:__________________________
b. No-Shrink Tee Company:_________________________
c. Which of these equations are proportional? Explain how you know.
3. Graph the costs for the two companies on the same coordinate axes. Include
labels, a title and a key.
4. For each company identify the y-intercept and the slope.
5. What does the y-intercept represent in the context of the problem?
6. What does the slope represent in the context of the problem?
7. For each company, what is the cost of 20 shirts? Which company would you
use?
Mighty T Company
No Shrink Tee Company
8. For each company, what is the cost of 35 shirts? Which company would you
use?
Mighty T Company
No Shrink Tee Company
9. Dr. Ferreira calculates that the school has $150 to spend on t-shirts. From
which company should she buy the t-shirts? Explain.
Mighty T Company
No Shrink Tee Company
10. For what number of t-shirts is the cost the same for the two companies?
How much is the cost?
11. When would it be best to use Mighty-Tee Company?
12. When would it be best to use No-Shrink Tee Company?
Name_______________________________
Date________________________
Using the Walkathon Money
Mrs. Brown’s class decides to use their money from the walkathon to provide
books for the children’s ward at the hospital. They put the money in the school
safe and withdraw a fixed amount each week to buy new books. To keep track
of the money, Isabella makes a table of the amount of money in the account at
the end of each week.
1. Create a graph using the table. Remember labels and a title!
a. What is the independent variable?
b. What is the dependent variable?
2. What is the initial value?
a.
What does it mean in the context of this problem?
3. How much money is withdrawn from the account each week?
4. Is the relationship between the number of weeks and the amount of
money left in the account a linear relationship? Explain.
5. a. Find the slope of the linear model.
b. Explain how you can find the slope from the table.
c. Explain how you can find the slope from the graph.
d. Is the slope increasing or decreasing? Explain how you know.
6. Write an equation that represents the relationship. Explain what each
number represents in the equation.