In Class 3
Name: _______________________ Block: __________
Algebra 2, Unit 1, Linear functions
I.
Fill in the blanks using the word bank.
Word Bank: opposite reciprocals, slope, same, linear
1. A ________________ function is a function whose graph is a straight line and has a constant rate of change.
2. The _______________ of the line is what measures its rate of change.
3. The rate of change (m) of a line is calculated by finding the change in y values divided by the change
in x values. This can be represented in two ways:
a) m =
△𝒚
△𝒙
This representation can be used when finding slope given a table of values or a graph.
𝒚 −𝒚
b) m = 𝒙 𝟐−𝒙𝟏 This representation can be used when finding slope given two points on the line.
𝟐
𝟏
4. Slope Intercept Form of the Equation of a Line : y = mx + b, where m is the slope and b is the y intercept.
Point Slope form: 𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏 ), where m is the slope and (𝑥1 , 𝑦1 ) is a point on the line.
Standard form: ax + by = c, where a, b and c are real numbers.
5. Slopes of parallel lines are the ________________.
6. Slopes of perpendicular lines are ____________________ ___________________
II. Determine if the relation represents a function and if it is linear. Also, find the slope and the equation
of the line.
1.
2.
x
0
0
0
0
y
1
3
5
9
Function: __________ Linear: _________
Function: __________ Linear: _________
Slope:
Slope:
Equation:
_______________________
_______________________
Equation:
_______________________
_______________________
In Class 3
Name: _______________________ Block: __________
Algebra 2, Unit 1, Linear functions
3.
x
y
0.5
9
1
1.5
6
3
2
0
4.
x
9
7
5
3
y
2
5
10
15
Function: __________ Linear: _________
Function: __________ Linear: _________
Slope:
Slope:
Equation:
_______________________
_______________________
Equation:
_______________________
_______________________
III. Find the intercepts of each line, draw the graph and label it to the right.
1. 5𝑥 + 𝑦 = −5
2. 6𝑥 + 2𝑦 = 6
IV. Write each function in slope intercept form. Graph and label to the right.
3. −3𝑥 − 𝑦 = 9
4. 4𝑥 + 3𝑦 = 6
In Class 3
Name: _______________________ Block: __________
Rule of four
Algebra 2, Unit 1, Linear functions
V. Write the equation of the line that meets the following criteria. Provide your answer in slope intercept
form.
3
5. The line parallel to 𝑦 = − 2 𝑥 + 4 and passes through the point (1, 5).
6. The line perpendicular to 𝑦 = −2 𝑥 + 11 and passes through (4, -2).
VI. Solve the story problems.
TOWING SERVICE
Verbal Description
When a tow truck is called, the cost of
the service is $10 plus $1 per mile that
the car must be towed.
Equation
Define your variables:
y=
x=
Write and graph a linear equation to
represent the total cost of the towing
service, which is dependent on the
number of miles the car is towed.
Write your equation:
y=
Find and interpret the slope and yintercept of the linear equation
Table of Values
X
Y
Graph
In Class 3
Name: _______________________ Block: __________
Rule of four
Algebra 2, Unit 1, Linear functions
T-SHIRT SHOP
Verbal Description
Equation
Your new job is at the Custom T Shop,
where T-shirts are printed to order. For
each order, Custom T Shop charges $8.00
per shirt plus a one time set up fee of
$15.00.
x=
Write and graph a linear equation to show
how the total cost of the T-shirts depends
on how many T-shirts are ordered
VII.
Write your equation:
y=
Table of Values
X
Define your variables:
y=
Graph
Y
Write your own problem that depicts a linear relationship in the real world. Extra credit for
creativity.
Topic:
Verbal Description
Equation
Define your variables:
y=
x=
Write your equation:
y=
Table of Values
X
Y
Graph