Linear Mastery Quiz Linear Mastery Quiz
Unit Assessment
Name:
Date:
Part I: Multiple Choice
Circle the correct answer for each question. Use the space below each question for any necessary scratch work.
1. Which set of ordered pairs represents a function?
A) {(1, 2), (1, 3), (1, 4), (1, 5)}
B) {(2, 1), (3, 2), (4, 4), (2, 5)}
C) {(1, 1), (2, 1), (3, 1), (4, 1)}
D) {(3, 2), (4, 3), (3, 1), (4, 3)}
2. What is the domain of the relation: {(4, 2), (1, 1), (0, 0), (1, -1), (4, -2)}?
A) {0, 1, 4}
B) {-2, -1, 0, 1, 2}
C) {-2, -1, 0, 1, 2, 4}
D) {0, 1, 2, 4}
3. What is the slope of the line represented by the equation \(3x + 4y = 24\)?
A) 3
B) 4
C) \(-\frac{3}{4}\)
D) \(\frac{4}{3}\)
4. Which equation represents a line that is parallel to \(y = \frac{1}{2}x - 5\)?
A) \(y = -2x + 4\)
B) \(y = \frac{1}{2}x + 10\)
C) \(y = -\frac{1}{2}x - 5\)
D) \(y = 2x - 5\)
5. Two lines are perpendicular if their slopes are:
A) Equal to each other
B) Reciprocals of each other
C) Opposite (negative) reciprocals of each other
D) Added together to equal zero
6. What is the slope of a line perpendicular to \(y = -3x + 7\)?
A) -3
B) 3
C) \(\frac{1}{3}\)
D) \(-\frac{1}{3}\)
7. Which equation is equivalent to \(2x - 4y = 8\)?
A) \(x - 2y = 4\)
B) \(4x - 8y = 12\)
C) \(y = 2x - 2\)
D) \(y = \frac{1}{2}x + 2\)
8. Write the equation of a line with a slope of 3 that passes through the point (2, 5).
A) \(y = 3x + 5\)
B) \(y = 3x - 1\)
C) \(y = 3x + 11\)
D) \(y = -3x + 11\)
9. What is the equation of the line that passes through (-1, 3) and (-2, 5)?
A) \(y = -2x + 1\)
B) \(y = 2x + 5\)
C) \(y = -2x - 1\)
D) \(y = 2x - 1\)
10. If \(f(x) = 2x^2 - 3x + 7\), what is the value of \(f(3)\)?
A) 16
B) 22
C) 28
D) 34
11. A line passes through (0, -4) and has a slope of 2. What is its equation in standard form?
A) \(2x - y = 4\)
B) \(2x + y = -4\)
C) \(y = 2x - 4\)
D) \(x - 2y = 8\)
12. Which statement correctly describes the lines \(y = 3x + 4\) and \(y = 3x - 2\)?
A) They are perpendicular.
B) They are the same line.
C) They are parallel.
D) They intersect at (0, 4).
13. The equation \(4y - 6x = 8\) has what slope?
A) -6
B) \(\frac{3}{2}\)
C) \(\frac{2}{3}\)
D) 8
14. Which point is the y-intercept of the graph of \(x + 3y = 6\)?
A) (0, 2)
B) (0, 6)
C) (0, 18)
D) (6, 0)
15. A landscaper sells bushes for $13 each and trees for $63 each. If total sales were $616, which equation models the number of bushes (\(b\)) and trees (\(t\)) sold?
A) \(63b + 13t = 616\)
B) \(13b + 63t = 616\)
C) \(b + t = 616\)
D) \(13b - 63t = 616\)
Part II: Open Ended
Show all work clearly. Box your final answer.
16. Determine the equation of a line that is perpendicular to the line \(y = \frac{1}{2}x - 3\) and passes through the point (-1, 4). Write your final answer in slope-intercept form.
17. You are in charge of buying food for a family reunion. You spend exactly $90 on hamburgers and turkey burgers. Each hamburger costs $1.50 and each turkey burger costs $2.00.
Part A
Write an equation in standard form that relates the number of hamburgers (\(x\)) and turkey burgers (\(y\)) you can purchase.
Part B
If you purchase 40 hamburgers, determine how many turkey burgers you can purchase. Show your algebraic work below.
Linear Mastery Classwork Packet Linear Mastery Packet
Classwork & Review
Name:
Date:
Do Now
1. Find the slope of the line that passes through the points (2, 3) and (-1, 4).
2. Convert the equation \(4x - 2y = 12\) into slope-intercept form (\(y = mx + b\)).
Guided Practice
Topic 1: Parallel and Perpendicular Logic
Recall: Parallel lines have the same slope. Perpendicular lines have opposite reciprocal slopes.
Given Slope
m = 4
Parallel Slope
Perpendicular Slope
Topic 2: Writing Equations
Example: Write the equation of a line perpendicular to \(y = -\frac{2}{3}x - 1\) that passes through (4, 3).
Independent Practice
3. Manuel has $15 to spend on apps and music. Apps cost $2 each and songs cost $1 each.
a) Write a linear equation in standard form representing this scenario (x = apps, y = songs).
b) Rewrite the equation in slope-intercept form.
c) If Manuel buys 4 apps, how many songs can he buy? Show your work.
4. Prove whether the following two equations represent lines that are parallel, perpendicular, or neither. Justify your answer.
y = -2x + 1
x - 2y = 6
Exit Ticket
5. Which of the following equations represents a line perpendicular to the line graphed below?
Line K (m = -1)
A) \(y = x + 4\)
B) \(y = -x + 2\)
C) \(y = 2x - 1\)
D) \(y = -\frac{1}{2}x + 3\)
Justification (Include slope comparison):
Linear Mastery Teacher Answer Key Teacher Answer Key
Linear Mastery Review & Assessment
SOLUTIONS
Quiz Solutions
1. C
2. A
3. C
4. B
5. C
6. C
7. A
8. B
9. A
10. A
11. A
12. C
13. B
14. A
15. B
Q16. Perpendicular Line through (-1, 4):
Original m = 1/2 \(\rightarrow\) Perp m = -2
y - 4 = -2(x + 1) \(\rightarrow\) y - 4 = -2x - 2
Final Answer: y = -2x + 2
Q17. Modeling reunion food:
a) \(\mathbf{1.5x + 2y = 90}\)
b) \(1.5(40) + 2y = 90 \rightarrow 60 + 2y = 90 \rightarrow 2y = 30 \rightarrow \mathbf{y = 15}\)
Classwork Monitoring Key
Do Now Solutions
1. \(m = \frac{4-3}{-1-2} = \mathbf{-\frac{1}{3}}\)
2. \(-2y = -4x + 12 \rightarrow \mathbf{y = 2x - 6}\)
Guided Practice Solutions
Topic 1: Parallel = 4; Perpendicular = -1/4
Topic 2: (Perp to -2/3 through 4,3) \(\rightarrow\) Perp m = 3/2; \(y - 3 = \frac{3}{2}(x - 4) \rightarrow \mathbf{y = \frac{3}{2}x - 3}\)
Independent Practice Solutions
3. Manuel's Scenario: a) \(2x + y = 15\). b) \(y = -2x + 15\). c) \(2(4) + y = 15 \rightarrow \mathbf{y = 7}\) songs.
4. Relationship: Perpendicular . Line 1: \(m = -2\). Line 2: \(-2y = -x + 6 \rightarrow y = \frac{1}{2}x - 3\). Slopes are -2 and 1/2.
Exit Ticket Master Answer
ANSWER: A
Justification: The graphed line has a slope of -1. Perpendicular lines must have opposite reciprocal slopes. The opposite reciprocal of -1 is +1. Only equation A has a slope of 1.
Homework Master Key
1. B (Parallel)
2. C (Perp m = -2)
3. C (m = -2/5)
4. C (x doesn't repeat)
5. B (y-int is 7)
6. B (Plug in 2,3)
7. Parallel Line:
\(y = 3x + 15\)
8. Conversion:
\(y = \frac{3}{2}x - 6\); \(m = 3/2, b = -6\)
9. Coins:
a) \(0.10d + 0.25q = 0.80\)
b) \(0.10d + 0.50 = 0.80 \rightarrow \mathbf{d = 3}\)
10. Vans:
a) \(8s + 12l = 144\)
b) \(8(15) + 12l = 144 \rightarrow \mathbf{l = 2}\)
Linear Mastery Homework Packet Linear Mastery Practice
Homework Assignment
Name:
Due Date:
Complete the following 10 questions. Show all necessary work in the provided scratch spaces.
Part I: Concept Review
1. Which relationship is true for the lines \(y = 3x + 1\) and \(y = 3x + 5\)?
A) They are perpendicular
B) They are parallel
C) They are the same line
D) They intersect at (0, 1)
2. Which equation represents a line that is perpendicular to \(y = \frac{1}{2}x - 3\)?
A) \(y = 2x + 4\)
B) \(y = \frac{1}{2}x + 3\)
C) \(y = -2x - 1\)
D) \(y = -\frac{1}{2}x - 3\)
3. What is the slope of a line parallel to the equation \(2x + 5y = 10\)?
A) 2
B) 5
C) \(-\frac{2}{5}\)
D) \(\frac{5}{2}\)
4. Which of the following sets of points represents a function?
A) {(1, 1), (1, 2), (1, 3)}
B) {(5, 1), (5, 2), (5, 3)}
C) {(1, 2), (2, 2), (3, 2)}
D) {(4, 1), (4, 4), (1, 4)}
5. What is the y-intercept of the line \(y - 3 = 4(x + 1)\)?
A) (0, 3)
B) (0, 7)
C) (0, -1)
D) (0, 4)
6. Which point lies on the line \(y = 2x - 1\)?
A) (1, 2)
B) (2, 3)
C) (0, 1)
D) (3, 4)
Part II: Application & Modeling
7. Parallel Logic: Write the equation of a line parallel to \(y = 3x - 5\) that passes through the point (0, 15).
8. Standard Form: Convert \(3x - 2y = 12\) into slope-intercept form. Identify slope (\(m\)) and y-intercept (\(b\)).
9. Coin Challenge: You have $0.80 in your backpack in dimes (\(d\)) and quarters (\(q\)).
Part A
Write an equation in standard form for this situation.
Part B
If you have 2 quarters, how many dimes do you have? Show your work.
10. Van Trip: A small van holds 8 people and a large van holds 12 people. Your class of 144 people needs transportation.
Part A
Write an equation that models the possible combination of small vans (s) and large vans (l).
Part B
If you use 15 small vans, how many large vans are needed? Show your algebraic work.
Linear Mastery Quiz Answer Key Quiz Answer Key
Linear Mastery Assessment
TEACHER ONLY
Confidential Document
I
Multiple Choice Solutions
15 Questions • 3 Points Each
Q1: C
Q2: A
Q3: C
Q4: B
Q5: C
Q6: C
Q7: A
Q8: B
Q9: A
Q10: A
Q11: A
Q12: C
Q13: B
Q14: A
Q15: B
II
Open Ended Step-by-Step
2 Questions • 10 Points Each
16
Perpendicular Line Equation
Logic: Slope Relations
Analysis
Step 1: Perp Slope (\(m\))
Original \(m = 1/2\). The perpendicular slope is the negative reciprocal.
\(m_{\perp} = -2\)
Computation
Step 2: Solve for \(b\) using (-1, 4)
\(y = mx + b\)
\(4 = -2(-1) + b\)
\(4 = 2 + b\)
\(b = 2\)
Final Answer \(y = -2x + 2\)
17
Reunion Budget Modeling
Logic: Linear Systems
Part A: Standard Form
Costs: $1.50 per hamburger (\(x\)), $2.00 per turkey burger (\(y\)). Total = $90.
\(1.5x + 2y = 90\)
Part B: Substitution (\(x=40\))
\(1.5(40) + 2y = 90\)
\(60 + 2y = 90\)
\(2y = 30\)
\(y = 15\)
Final Answer 15 Turkey Burgers
Part I Score
45 Points
Part II Score
20 Points
Total Possible
65 PTS
Linear Mastery Cumulative Test Cumulative Mastery Test
Unit 7 • Final Summative
Name:
Date:
Part I: Multiple Choice (Questions 1-25)
1. Which set of ordered pairs represents a function?
A) {(1, 2), (1, 3), (1, 4), (1, 5)}
B) {(2, 1), (3, 2), (4, 4), (2, 5)}
C) {(1, 1), (2, 1), (3, 1), (4, 1)}
D) {(3, 2), (4, 3), (3, 1), (4, 3)}
2. If \(f(x) = x^2 + 5\), what is the range for the domain {0, 2}?
A) {5, 9}
B) {0, 4}
C) {5, 7}
D) {0, 5}
3. What is the slope of the line that passes through (2, 6) and (-2, 4)?
A) 2
B) 1/2
C) -1/2
D) 0
4. Which graph represents a function with a negative slope and a positive y-intercept?
A) \(y = 2x + 3\)
B) \(y = -2x - 3\)
C) \(y = -2x + 3\)
D) \(y = 2x - 3\)
5. What is the slope of the line represented by the equation \(3x + 4y = 24\)?
A) 3
B) 4
C) -3/4
D) 4/3
6. Identify the type of correlation: "As study hours increase, exam scores tend to increase."
A) Positive
B) Negative
C) None
D) Constant
7. Which equation represents a line of best fit for data that shows a negative linear association?
A) \(y = 0.5x + 10\)
B) \(y = -2.4x + 25\)
C) \(y = 15\)
D) \(y = x^2\)
8. Which equation represents a line that is parallel to \(y = \frac{1}{2}x - 5\)?
A) \(y = -2x + 4\)
B) \(y = \frac{1}{2}x + 10\)
C) \(y = -\frac{1}{2}x - 5\)
D) \(y = 2x - 5\)
9. Translate: "Six less than twice a number is 10."
A) \(6 - 2n = 10\)
B) \(2n - 6 = 10\)
C) \(2(n - 6) = 10\)
D) \(6 < 2n + 10\)
10. Connor can spend at most $16 at the carnival. Admission is $4.50 and rides are $0.79 each. Which inequality solves for rides (\(r\))?
A) \(4.50 + 0.79r \le 16\)
B) \(4.50r + 0.79 \le 16\)
C) \(4.50 + 0.79r < 16\)
D) \(4.50 + 0.79r \ge 16\)
11. What is the value of \(y\) if \(2y - 7 = 18\)?
A) 5.5
B) 12.5
C) 25
D) 11
12. Which point is on the line \(y = 2x + 3\)?
A) (0, 0)
Linear Mastery Prep 7.9 Classwork Packet Cumulative Mastery Packet
Lesson 7.9 • Test Prep & Review
Name:
Date:
Do Now: Unit Warm-Up
1. Determine the range of \(f(x) = x^2\) for the domain {-1, 0, 1, 2}.
2. Find the slope of the line passing through (2, 3) and (-1, 4).
3. Identify the correlation: "The more ice cream sold, the higher the outside temperature."
4. Convert \(3x - 2y = 12\) into slope-intercept form (\(y = mx + b\)).
Guided Practice: Complex Modeling
Task 1: Inequality Logic
Scenario: Mr. Roberts has a $4000 budget for a vacation. Flights cost $1800 total, and the hotel is $110 per night.
A) Define variable & set up inequality:
B) Solve for maximum number of nights:
Task 2: Interpreting Best Fit
Car Mass (kg)
Fuel Economy (MPG)
The equation of best fit is \(y = -0.01x + 35\). Explain what the slope (-0.01) represents in terms of mass and fuel economy.
Independent Practice: Cumulative Challenge
1. Which relationship represents a linear function?
A) \(y = 3^x - 5\)
B) \(y = x^2 + 10\)
C) \(x = 4y + 12\)
D) \(y = 1/x\)
2. What is the x-intercept of the equation \(x + 3y = 6\)?
A) (0, 2)
B) (6, 0)
C) (2, 0)
D) (-6, 0)
3. Write the equation of a line perpendicular to \(y = -2x + 1\) that passes through (4, 5).
4. Which graph would show a "Strong Negative Correlation"?
A) Points form a tight line going up.
B) Points form a tight line going down.
C) Points are scattered with no pattern.
D) Points form a wide U-shape.
5. A line of best fit for heart rate (\(x\)) and oxygen uptake (\(y\)) is \(y = 0.05x - 3.5\). Predict \(y\) if \(x = 120\).
6. Solve for \(n\): "A number increased by 7 is less than 16."
A) \(n + 7 < 16 \rightarrow n < 9\)
B) \(n + 7 > 16 \rightarrow n > 9\)
C) \(7n < 16 \rightarrow n < 2.3\)
D) \(n - 7 < 16 \rightarrow n < 23\)
7. If \(f(x) = 2x^2 - 3x + 7\), evaluate \(f(-2)\). Show all steps clearly.
8. Which equation has NO solution?
A) \(2x + 1 = 2x + 1\)
B) \(x + 5 = x - 5\)
C) \(3x = 0\)
D) \(x = -5\)
9. Trinity saves $60 + $15 per week. Write an inequality showing she needs at least $500.
Linear Mastery Cumulative Homework Packet Cumulative Homework
Test Readiness Assignment
Name:
Due Date:
Complete the following 10 questions. Show all necessary work.
Part I: Mixed Review (MC)
1. Which equation represents a line with a slope of 1/2 passing through (2, 6)?
A) \(y = 1/2x + 5\)
B) \(y = 1/2x + 6\)
C) \(y = 2x + 5\)
D) \(y = x + 5\)
2. If a scatter plot has "No Correlation", what would it look like?
A) Points form a straight line up
B) Points are scattered randomly
C) Points form a curve
D) Points form a straight line down
3. Solve the inequality: \(3.50 + 3x \le 20\)
A) \(x \le 5.5\)
B) \(x \le 4.7\)
C) \(x \ge 5.5\)
D) \(x < 5\)
4. What is the value of \(f(4)\) for \(f(x) = x^2 + 3\)?
A) 11
B) 19
C) 7
D) 16
5. Which of the following is NOT a linear function?
A) \(y = 3x - 1\)
B) \(y = x^2\)
C) \(2x + 4y = 8\)
D) \(y = 5\)
Part II: Test Prep Open Ended
6. Parallel Lines: Write an equation for a line parallel to \(y = 3x + 1\) that passes through the point (2, 10).
7. Scatter plot Prediction: A line of best fit for height (\(x\)) and weight (\(y\)) is \(y = 4x + 87\). Predict the weight of a person who is 6 feet tall (\(x = 6\)).
8. Inequality Scenario: Ms. Hills has $70. She buys 3 notebooks for $5 each. Calculators cost $18 each. How many calculators can she buy at most? Write and solve an inequality.
9. Range Check: Determine the range of \(f(x) = 2x + 5\) given the domain {-2, 0, 2}.
10. Graphing Mastery: Sketch the function \(y = -2x + 3\).
Identify Slope (\(m\))
Identify Y-Intercept (\(b\))
Cumulative Test and Homework Answer Key Mastery Test Answer Key
Linear Unit Final • Teacher Reference
SOLUTIONS
I
Multiple Choice Solutions (25 PTS)
1. C
2. A
3. B
4. C
5. C
6. A
7. B
8. B
9. B
10. A
11. B
12. B
13. B
14. C
15. A
16. B
17. C
18. C
19. A
20. B
21. B
22. B
23. B
24. B
25. B
II
Open Ended Step-by-Step
Q26. Perpendicular Relations
• Original slope: \(m = 1/2\). Perpendicular slope: \(m_{\perp} = -2\).
• Using \((-1, 4)\): \(4 = -2(-1) + b \rightarrow 4 = 2 + b \rightarrow b = 2\).
ANSWER: \(y = -2x + 2\)
Q27. Linear Modeling
• Part A Equation: \(1.5x + 2y = 90\)
• Part B Substitution: \(1.5(40) + 2y = 90 \rightarrow 60 + 2y = 90 \rightarrow y = 15\).
ANSWER: 15 turkey burgers.
Q28. Data Interpretation
• Slope (0.05): For every 1 BPM increase in heart rate, oxygen uptake increases by 0.05 liters/min.
• Prediction: \(y = 0.05(150) - 3.5 = 7.5 - 3.5 = 4\).
ANSWER: 4.0 liters per minute.
Q29. Inequality Modeling
• Part A Inequality: \(60 + 15w \ge 500\)
• Part B Evaluation: \(60 + 15(25) = 435\). Since \(435 < 500\), she does NOT have enough.
ANSWER: No, she will be $65 short.
Cumulative Homework Master Key
1. A: \(y = 1/2x + 5\) (Slope 1/2, check pt: 6 = 1/2(2) + 5)
2. B: Points are scattered randomly with no trend.
3. B: \(3x \le 16.5 \rightarrow x \le 5.5\). Max 5 items.
4. B: \(4^2 + 3 = 16 + 3 = 19\)
5. B: \(y = x^2\) (Quadratic, not linear)
6. \(y = 3x + 4\): Same slope (3). \(10 = 3(2) + b \rightarrow b = 4\).
7. 111 lbs: \(y = 4(6) + 87 = 24 + 87 = 111\).
8. \(15 + 18c \le 70\): \(18c \le 55 \rightarrow c \le 3.05\). Max: 3 calculators.
9. Range: {1, 5, 9}: \(2(-2)+5=1\); \(2(0)+5=5\); \(2(2)+5=9\).
Lesson 7.9 Prep Packet Answer Key Prep Packet Answer Key
Lesson 7.9 • Cumulative Practice Review
TEACHER ONLY
Do Now Solutions
1. Range: {0, 1, 4}
2. Correlation: Positive Correlation.
3. Correlation: Positive Correlation.
4. Conversion: \(y = 1.5x - 6\)
Guided Practice Key
Task 1: Vacation Budget
• Inequality: \(1800 + 110n \le 4000\)
• Solving: \(110n \le 2200 \rightarrow n \le 20\). Max 20 nights.
Task 2: Fuel Efficiency Slope
• Meaning: For every 1 kg increase in mass, the fuel economy decreases by 0.01 MPG.
Independent Practice Master Grid
1. C (\(x = 4y + 12\) is linear)
2. B (Plug in \(y = 0 \rightarrow x = 6\))
3. \(y = 1/2x + 3\) (Check: \(5 = 1/2(4) + 3\))
4. B (Tight line going down)
5. 2.5 (Substitute: \(0.05(120) - 3.5 = 6 - 3.5\))
6. A (\(n < 9\))
7. 21 (\(2(4) - 3(-2) + 7 \rightarrow 8 + 6 + 7 = 21\))
8. B (\(x+5 = x-5 \rightarrow 5 = -5\) is False)
9. \(60 + 15w \ge 500\)
10. B (12.5)
Exit Ticket Guidance
A) Scenario: Student should create a situation with a $50 fixed fee and $15 recurring cost (e.g., $50 joining fee and $15 per session for a gym). Max budget is $200.
B) Explanation: A linear function represents an exact, predictable rule for every input. A scatter plot with a linear trend shows a correlation where data points roughly follow a path but are not perfectly aligned.
