Unit 3 – Graphing Linear Equations 1
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– Unit 3b – [Graphing Linear Equations]
Unit 3 – Graphing Linear Equations 2
To be a Successful Algebra class,
TIGERs will show…
#TENACITY during our practice, have…
I attempt all practice I attempt all homework I never give up when I don’t understand
#INTEGRITY as we help others with their work, maintain a…
I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them
#GO-FOR-IT attitude, continually…
I write down all notes, even if I’m confused I remain positive about my goals I treat each day as a chance to reset
#ENCOURAGE each other to succeed as a team, and always…
I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up
#REACH-OUT and ask for help when we need it!
I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to
Unit 3 – Graphing Linear Equations 3
Unit Calendar
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
October 20 21 22 23 24
…
…
…
Direct Variation Parallel and
Perpendicular Slopes
/ Lines
27 28 29 30 31
Applications
Matching Activity
QUIZ
Applications of Lines
Applications of Lines Review
TEST
September 3 4 5 6 7
Unit 3 Task
In – Class Project
Review 6-Weeks TEST
Graphing Activity Early Release
Essential Questions
What does it mean for relationship to be a linear function?
How can linear functions be used to model problem situations?
What are the critical features of a graph and how can they help me solve this problem?
How can a value of a function be represented?
What is the meaning of slope and how do I find it in this situation?
Unit 3 – Graphing Linear Equations 4
Critical Vocabulary
Linear Function
Parent Function
Slope
x-Intercept / Zero
y-intercept
Direct Variation
Parallel
Perpendicular
Unit 3 – Graphing Linear Equations 5
Direct Variation
What is Direct Variation? Direct Variation Equation: Constant of Variation: Table: Graph:
𝑥 𝑦
Unit 3 – Graphing Linear Equations 6
Applications: You buy several markers for 70 cents each. Write the function rule to describe the cost of buying markers. The number of pumpkins sold at Peter’s Pumpkin Patch varies directly with the amount of days until Halloween. If 15 days before halloween they sell 120 pumpkins, predict how many pumpkins they will sell 6 days before halloween.
Write the Equation:
The point (5, -20) is on the graph of a direct variation. Write the equation for the function.
Find the missing coordinate:
The following points vary directly with each other. Find the missing coordinate. (1, 𝑦) 𝑎𝑛𝑑 (2,14)
Unit 3 – Graphing Linear Equations 7
Unit 3 – Graphing Linear Equations 8
Practice: Applications:
You’re ordering pizzas for $12 each. Write the function rule to describe the cost of buying pizzas. A given function is written so that y varies directly with x. Write the direct variation equation if y is 36 when x is 4.
Write the Equation:
The point (-3, 18) is on the graph of a direct variation function. Write the equation for the function.
Find the missing coordinate:
The following points vary directly with each other. Find the missing coordinate. (𝑥, 10) 𝑎𝑛𝑑 (9, 6)
Unit 3 – Graphing Linear Equations 9
Parallel and Perpendicular Slopes
𝑦 =1
3𝑥 − 2
𝑦 =1
3𝑥 + 3
𝑦 = −4𝑥 + 3
𝑦 = −4𝑥
𝑦 = 5
𝑦 = −2
𝑦 =4
3𝑥 + 1
𝑦 = −3
4𝑥 + 5
𝑦 = −2
3𝑥 − 1
𝑦 =3
2𝑥 + 4
𝑦 =1
2𝑥 + 3
𝑦 = −2𝑥 + 4
2 Lines are parallel if the slopes are ____ _______. 2 Lines are perpendicular if the slopes are _________ ____________.
(Flip the _________, Flip the _________) Otherwise, the lines are called ________________.
Unit 3 – Graphing Linear Equations 10
Examples: State if the pairs of lines are Parallel, Perpendicular or Intersecting. From Equations:
3𝑥 + 2𝑦 = 6 2𝑥– 3𝑦 = 12
2𝑥 + 𝑦 = 4 𝑥 + 2𝑦 = 4
From Ordered Pairs: Line containing ( 10, 1 ),( -5, -2 ) and Line containing ( 3, 10 ),( -4, -4 )
Line containing ( -4, 13 ),( 3, -8 ) and Line containing ( 2, -4 ),( -1, 5 )
Practice:
𝑦 =1
4𝑥 + 2
𝑦 =𝑥
4+ 5
𝑦 = 3𝑥 + 4
𝑦 =1
3𝑥 − 6
𝑥 = 2
𝑦 = −3
𝑦 = 4
𝑦 = 6
𝑦 = 3𝑥 − 5
𝑦 = −𝑥
3+ 2
𝑦 = 2𝑥 + 5
𝑦 = 5𝑥 + 2
Unit 3 – Graphing Linear Equations 11
𝑦 =1
2𝑥 + 2 − 2𝑥 + 𝑦 = 6
−3𝑥 + 2𝑦 = 4 2𝑥 + 3𝑦 = −3
Line containing ( 5, 8 ), ( 10, 12 ) and Line containing ( 0, -3 ), ( 4, -8 )
Line containing ( -4, 6 ), ( -2, 7 ) and Line containing ( 3, 10 ), ( 13, 14 )
6𝑥 + 𝑦 = 12 − 12𝑥 − 2𝑦 = 14
10𝑥 + 2𝑦 = 4 2𝑥 + 10𝑦 = 40
Line containing ( 3, 5 ), ( -6, 5 ) and Line containing ( 4, 7 ), ( 1, 7 )
Line containing ( 5, 8 ), ( 9, 8 ) and Line containing ( 3, -3 ), ( 3, 4 )
Unit 3 – Graphing Linear Equations 12
Unit 3 – Graphing Linear Equations 13
Applications of Lines
Examples: I owe my friend $10 and I plan to pay them back $2 each day. The equation that models this situation is
𝑦 = 2𝑥 – 10
A) What does the y represent?
B) What does the x represent?
C) What does the 2 represent?
D) What does the 10 represent?
E) Why is the 10 negative in this problem?
F) Would this be continuous or discrete?
G) Graph the equation
H) What is a reasonable domain for this problem?
Gina has a $30 gift card to Starbuck’s. Every time she buys a coffee she is charged $3.
A) Write an equation in Slope-Intercept Form to represent the problem
B) Why did you choose the sign of 3 to be positive or negative?
C) If we doubled the constant in the equation, what would that represent in the problem?
D) What is a reasonable domain for this situation?
E) Is this situation discrete or continuous?
Unit 3 – Graphing Linear Equations 14
Practice:
Chris does a lot of babysitting. When parents drop off their children and Chris can supervise at home, the
hourly rate is $3. If Chris has to travel to the child’s home, there is a fixed charge of $5 for transportation in
addition to the $3 hourly rate.
A) Write an equation for when he watches the
kids at home?
B) Write an equation for when he needs to travel to watch the kids?
C) Graph both Lines
D) Will a parent dropping off their kid ever pay more than if Chris has to travel to their home?
E) If in 3 years, Chris has a new equation, y = 5x + 10, what has changed in this problem?
The charges for Anderson’s Plumbing can be modeled by the following equation, where, C, is the total cost for
plumbing services that last, h, hours:
40 25C h
A) What does the 25 represent in this situation? B) What does the 40 represent in this situation?
The cost of dinner at a sweet 16 party is $300 plus $10 per person.
A) What is the equation that models this situation?
B) What does the y-intercept represent? C) What does the slope represent?
D) Find the cost for 50 guests.
Unit 3 – Graphing Linear Equations 15
Laura is on a 2 day hike in the Smoky Mountains. She hiked 8 miles the first day and is hiking at a rate of
3 mi/h on the second day. Her total distance is a function of the time she hikes.
A) What is the equation that models this situation?
B) What does the y-intercept represent? C) What does the slope represent?
D) What will be Laura’s total distance if she hikes 6 hours on the second day?
The equation for a car driving away from Katy is represented by the equation: 46y x , where y is the
distance from Katy after x hours.
A) What does y represent in this problem?
B) What does x represent in this problem?
C) What is the meaning of the slope?
D) What would the slope and y-intercept in the equation 46 184y x represent?
The Star Car Rental Company charges a flat fee of $30 plus $0.25 per mile to rent a car.
A) Which value would be considered the y-intercept or beginning value?
B) Which value would be considered the slope or rate of change?
C) Write the equation for this situation.
D) If you only had $50 to spend on the rental car, how many miles could you drive?
Unit 3 – Graphing Linear Equations 16
Applications of Lines
Unit 3 – Graphing Linear Equations 17
Unit 3 – Graphing Linear Equations 18
Extra Practice
Equation: y = 2x – 4 Table Graph
x y
-1
0
1
2
3
Equation: y = -4x + 3 Table Graph
x y
-1
0
1
2
3
Equation: y = 3x Table Graph
x y
-1
0
1 2
3
Equation: y = -x + 5 Table Graph
x y
-1
0
1 2
3
Equation: y = 1/3x – 4 Table Graph
x y
-3
0
3
6
9
Equation: y = -3/2x + 4 Table Graph
x y
-2
0
2
4
6
Unit 3 – Graphing Linear Equations 19
Answers:
Unit 3 – Graphing Linear Equations 20
Extra Practice
3x + 2y = 8
-2x + 3y = -15
-2x + 6y = 6
-3x - 4y = -8
10x + 5y = 25
-x - y = -4
Unit 3 – Graphing Linear Equations 21
Answers:
𝑦 = −3
2𝑥 + 4
𝑦 =2
3𝑥 − 5 𝑦 =
1
3𝑥 + 1
𝑦 = −3
4𝑥 + 2
𝑦 = −2𝑥 + 5 𝑦 = −𝑥 + 4
Unit 3 – Graphing Linear Equations 22
Unit 3 – Graphing Linear Equations 23
