Linear Functions Practice Test
Algebra 1 • Unit 4 Practice Assessment
Linear Functions & Equations
Name:
Date:
Period:
Score:
/ 100
Directions: Read each question carefully. Select the best answer or complete the designated blanks. Show all necessary work.
Page 1 of 5
1
A graph of a linear function is shown on the coordinate grid below.
x y 2 4 -2 -4 2 4 -2 -4
Write an equation in slope-intercept form that best represents this graph. Fill in the blanks below.
y = x +
2
The Oakridge High Drama Guild hosted a spring musical showcase to raise funds for stage lighting equipment. They spent $220 on printed playbills and $360 on costume rentals and stage set construction. Each general spectator ticket to the showcase was sold for $12. Which linear function represents the total profit, y, the drama guild makes if they sell x tickets?
A. y = 12x + 580
B. y = 580x − 12
C. y = 12x − 580
D. y = 12x − 360
3
Which equation describes the line through the points (4, −1) and (7, 5) in point-slope form?
A. y + 1 = 2(x − 4)
B. y − 1 = −2(x + 4)
C. y − 5 = ½(x − 7)
D. y + 5 = −½(x − 7)
Algebra 1 • Unit 4: Linear Functions Practice Test Turn page for Questions 4–6
Unit 4: Linear Functions Exam Practice Page 2 of 5
4
The first five terms of an arithmetic sequence are shown below:
a₁ = 34 a₂ = 26 a₃ = 18 a₄ = 10 a₅ = 2
Select the correct numbers from the bank below to create an equation that can be used to find the nth term of the sequence, an. Not all numbers will be used.
−8 8 −34 34 42 −42
an =
n +
5
What is the equation in slope-intercept form of the line that crosses the x-axis at 6 and is perpendicular to the line represented by y = −¾x + 2?
A. y = −¾x + 6
B. y = ⁴⁄₃x − 8
C. y = −¾x − 8
D. y = ⁴⁄₃x + 6
6
The graph of a horizontal line is shown on the coordinate plane below.
What is the equation and the slope of the line? Select the correct values from the tile options. Not all options will be used.
x y 4 -4 4 -4
x = 3 y = 3 y = 3x undefined 0 3
Slope:
Equation:
Algebra 1 • Unit 4: Linear Functions Practice Test Turn page for Questions 7–10
Unit 4: Linear Functions Exam Practice Page 3 of 5
7
Which equation in point-slope form best describes the line that is parallel to y = ⁴⁄₃x − 5 and passes through the point (3, −8)?
A. y + 8 = ⁴⁄₃(x − 3)
B. y + 8 = −⁴⁄₃(x − 3)
C. y + 8 = ¾(x − 3)
D. y + 8 = −¾(x − 3)
8
Marcus works as a mobile pet groomer. His total charge, C, for a grooming appointment is based on the number of hours spent grooming, h, at his standard rate of $24.50 per hour, plus a fixed $20 travel and sanitization fee. Which equation best describes the relationship between his total charge, C, and hours worked, h?
A. C = 20h + 24.50
B. C = 24.50h + 20
C. C = 24.50h + 20h
D. C = 24.50h
9
The graph models the linear relationship between the number of hours since draining began on a community reservoir and the remaining water volume in gallons.
Reservoir Water Volume 25,000 20,000 15,000 10,000 5,000 0 10 20 30 40 50 Draining Time (Hours) Remaining Volume (gal) (8, 18,000) (20, 12,000)
Write an equation that best represents this situation.
y = x +
10
The table represents some points on the graph of a linear function. Which function represents this relationship?
A. y = ⁵⁄₄x + 3
B. y = ⁵⁄₄x − 7
C. y = ⁴⁄₅x + 8
D. y = ⁴⁄₅x − 4
Algebra 1 • Unit 4: Linear Functions Practice Test Turn page for Questions 11–13
Unit 4: Linear Functions Exam Practice Page 4 of 5
11
An event hall charges a flat setup and cleaning fee plus a constant hourly rental rate. One organization booked the venue for 3 hours for a total cost of $295. Another organization booked the venue for 7 hours for a total cost of $555. Which linear equation represents the total cost in dollars, y, for renting the hall for x hours?
A. y = 20x + 235
B. y = 85x
C. y = 65x + 100
D. y = 65x + 195
12
Which equation is equivalent to 4x − y = 11 when solved for y?
A. y = −4x + 11
B. y = −4x − 11
C. y = 4x + 11
D. y = 4x − 11
13
Graph the following linear function: −2y = −3x + 4. Show your algebraic work to solve for slope-intercept form, then correctly plot at least TWO points on the coordinate plane and connect them with a straight line.
Show algebraic steps:
x y 2 4 -2 -4 2 4 -2 -4
Algebra 1 • Unit 4: Linear Functions Practice Test Turn page for Questions 14–16
Unit 4: Linear Functions Exam Practice Page 5 of 5
14
The values in the table represent a linear relationship between x and y. What is the rate of change of y with respect to x?
| x |
−5.5 |
−1.5 |
2.5 |
6.5 |
11.5 |
| y |
38 |
22 |
6 |
−10 |
−30 |
A. 16
B. −4
C. −8
D. 24
Use the graph below to answer Questions 15 and 16. The graph displays line m and point P.
x y -6 6 6 -6 m P
15
Which equation best represents the slope-intercept form of a line that passes through point P and is parallel to line m?
A. y = ½x + 2
B. y = −½x + 4
C. y = −½x − 1
D. y = ½x + 4
16
Constructed Response: Explain how you determined the equation of the line that passes through point P and is parallel to line m. Complete your explanation using the sentence stem below.
Sentence Stem: I determined the equation of the new line by...
Algebra 1 • Unit 4: Linear Functions Practice Test End of Assessment • Verify all responses
Linear Functions Answer Key
Algebra 1 • Teacher Resource
Practice Test Answer Key & Worked Solutions
Unit 4: Linear Functions
Quick Reference Answer Key Total Points: 100
Q13x − 2
Q2C
Q3A
Q4−8n + 42
Q5B
Q60 / y = 3
Q7A
Q8B
Q9−500x+22000
Q10B
Q11C
Q12D
Q13y=1.5x−2
Q14B (−4)
Q15B
Q16Rubric
Step-by-Step Worked Solutions: Questions 1–4
1 Slope-Intercept Form from Graph
Answer: y = 3x + (−2) or y = 3x − 2
Step 1 (Identify y-intercept): The line intersects the vertical y-axis at (0, −2), so b = −2.
Step 2 (Calculate slope): Locate another integer lattice point on the line, such as (1, 1) or (2, 4).
m = (y₂ − y₁) / (x₂ − x₁) = (1 − (−2)) / (1 − 0) = 3 / 1 = 3
Conclusion: Substituting m = 3 and b = −2 yields y = 3x − 2. In the blank format: y = [3]x + [−2].
2 Linear Profit Function
Correct Option: C
Analysis: Profit is defined as Total Revenue − Total Costs.
- Revenue generated from selling x tickets at $12 each = 12x
- Total fixed expenses = $220 (playbills) + $360 (costumes & set) = $580
Therefore, profit y = 12x − 580. Distractor A adds expenses instead of subtracting; distractor B reverses rate and constant; distractor D only includes costume costs.
3 Point-Slope Form from Two Points
Correct Option: A
Given points: (x₁, y₁) = (4, −1) and (x₂, y₂) = (7, 5).
m = (5 − (−1)) / (7 − 4) = 6 / 3 = 2
In point-slope form: y − y₁ = m(x − x₁). Using point (4, −1): y − (−1) = 2(x − 4), which simplifies to y + 1 = 2(x − 4).
4 Arithmetic Sequence as Linear Function
Answer: an = −8n + 42
Sequence: 34, 26, 18, 10, 2... First term a₁ = 34.
Common difference: d = a₂ − a₁ = 26 − 34 = −8.
aₙ = a₁ + (n − 1)d = 34 + (n − 1)(−8) = 34 − 8n + 8 = −8n + 42
The selected tiles from the bank are −8 (placed before n) and 42 (constant term).
Algebra 1 • Unit 4: Linear Functions Worked Solutions Page 1 of 4 • Continue to Solutions 5–9
Unit 4: Linear Functions Exam Solutions Page 2 of 4
Step-by-Step Worked Solutions: Questions 5–9
5 Perpendicular Line Equation
Correct Option: B
Step 1: The given line is y = −¾x + 2, which has slope m₁ = −¾.
Step 2: Perpendicular lines have negative reciprocal slopes: m₂ = −1 / (−¾) = ⁴⁄₃.
Step 3: The line crosses the x-axis at 6, meaning it passes through the coordinate point (6, 0).
y − 0 = ⁴⁄₃(x − 6) ⟹ y = ⁴⁄₃x − ⁴⁄₃(6) ⟹ y = ⁴⁄₃x − 8
6 Horizontal Line Properties
Slope: 0 | Equation: y = 3
Slope: A horizontal line has zero vertical change (Δy = 0) as x varies. Thus, m = 0 / Δx = 0.
Equation: Every point along the line has a fixed y-coordinate of 3. The equation is y = 3. (Note: vertical lines have undefined slope and equations of form x = c).
7 Parallel Line in Point-Slope Form
Correct Option: A
Parallel lines share identical slopes. The given line y = ⁴⁄₃x − 5 has slope m = ⁴⁄₃.
Using point (x₁, y₁) = (3, −8) in point-slope form: y − (−8) = ⁴⁄₃(x − 3), which simplifies directly to y + 8 = ⁴⁄₃(x − 3).
8 Modeling Linear Word Problem
Correct Option: B
Marcus charges an hourly rate of $24.50 per hour worked, representing the rate of change (slope) = 24.50h.
The one-time fixed travel/sanitization fee is $20 (y-intercept). Combining these gives C = 24.50h + 20.
9 Linear Equation from Real-World Graph
Answer: y = −500x + 22,000
Points from graph: (8, 18000) and (20, 12000).
m = (12,000 − 18,000) / (20 − 8) = −6,000 / 12 = −500 gal/hour
Solve for initial volume (b):
y = mx + b ⟹ 18,000 = −500(8) + b ⟹ 18,000 = −4,000 + b ⟹ b = 22,000
The equation modeling remaining water volume is y = −500x + 22,000.
Algebra 1 • Unit 4: Linear Functions Worked Solutions Page 2 of 4 • Continue to Solutions 10–13
Unit 4: Linear Functions Exam Solutions Page 3 of 4
Step-by-Step Worked Solutions: Questions 10–13
10 Linear Function from Table of Points
Correct Option: B
Pick any two pairs: (−8, −17) and (4, −2).
m = (−2 − (−17)) / (4 − (−8)) = 15 / 12 = ⁵⁄₄
Now find b using (4, −2):
y = mx + b ⟹ −2 = ⁵⁄₄(4) + b ⟹ −2 = 5 + b ⟹ b = −7
Verify with third point (16, 13): y = ⁵⁄₄(16) − 7 = 20 − 7 = 13 (correct). Equation is y = ⁵⁄₄x − 7.
11 Two-Point Word Problem
Correct Option: C
Translate information into coordinate points (hours, total cost): (3, 295) and (7, 555).
Hourly Rate (m) = (555 − 295) / (7 − 3) = 260 / 4 = $65 per hour
Solve for flat setup fee b using (3, 295):
295 = 65(3) + b ⟹ 295 = 195 + b ⟹ b = 100
The linear function representing total rental cost is y = 65x + 100.
12 Solving Standard Form for y
Correct Option: D
4x − y = 11
−y = −4x + 11 (Subtract 4x from both sides)
y = 4x − 11 (Multiply or divide entire equation by −1)
Common student error: forgetting to distribute division by −1 to both terms on the right side, leading to distractor A or C.
13 Graphing Linear Function
y = ³⁄₂x − 2
Algebraic Solution:
−2y = −3x + 4
y = (−3x + 4) / (−2)
y = ³⁄₂x − 2
Key Features:
• y-intercept: (0, −2)
• Slope: m = ³⁄₂ (rise 3, run 2)
• Plotted Points: (0, −2), (2, 1), (4, 4), (−2, −5)
Algebra 1 • Unit 4: Linear Functions Worked Solutions Page 3 of 4 • Continue to Solutions 14–16
Unit 4: Linear Functions Exam Solutions Page 4 of 4
Step-by-Step Worked Solutions: Questions 14–16
14 Rate of Change from Decimal Table
Correct Option: B (−4)
Select any two pairs from the table, for example (−5.5, 38) and (−1.5, 22):
Rate of change = Δy / Δx = (22 − 38) / (−1.5 − (−5.5)) = −16 / 4 = −4
Verify with next interval from (6.5, −10) to (11.5, −30): Δy / Δx = (−30 − (−10)) / (11.5 − 6.5) = −20 / 5 = −4. The constant rate of change is −4.
15 Parallel Line Through Given Point
Correct Option: B (y = −½x + 4)
Find slope of line m: Line m passes through coordinates (−2, 0) and (0, −1).
m = (−1 − 0) / (0 − (−2)) = −1 / 2 = −½
Write equation through Point P(2, 3): Parallel slope is also m = −½.
y − 3 = −½(x − 2) ⟹ y − 3 = −½x + 1 ⟹ y = −½x + 4
16 Constructed Response Rubric & Exemplar
Scoring Weight: 4 Points
Exemplar Student Response:
“I determined the equation of the new line by first finding the slope of line m using points (−2, 0) and (0, −1), which gave a slope of −½. Because parallel lines have the same slope, the new line must also have m = −½. Next, I identified the coordinates of point P as (2, 3) and substituted both the slope and point into point-slope form: y − 3 = −½(x − 2). Finally, I solved for y by distributing −½ to get y − 3 = −½x + 1, and added 3 to both sides to find the slope-intercept equation y = −½x + 4.”
| Score |
Performance Criteria |
| 4 Points |
Correctly identifies slope of line m as −½; states parallel lines have equal slopes; identifies point P as (2, 3); shows complete algebraic work leading to y = −½x + 4. |
| 3 Points |
Identifies correct slope and coordinates of P, but makes a minor sign or arithmetic error when solving for y-intercept, OR provides correct final equation with slightly incomplete justification. |
| 2 Points |
States parallel lines have equal slope and finds slope −½, but misidentifies coordinates of P or fails to construct the equation. |
| 1 Point |
Identifies point P or calculates an incorrect slope, showing minimal conceptual understanding of parallel lines. |
| 0 Points |
No relevant work shown, blank, or completely incorrect response. |
Algebra 1 • Unit 4: Linear Functions Worked Solutions Page 4 of 4 • End of Answer Key
