Algebra 1 Practice Test: Linear Functions, Slope and Graphs
- Linear Functions, Slope and Graphs
- 15 questions
- 20 minutes
These 15 questions practice slope, intercepts, slope-intercept and point-slope form, parallel and perpendicular lines, function notation, tables, graphs and real-world rates of change. Slope is the change in y divided by the change in x, always in that order.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the slope of the line through the points (−2, 5) and (4, −7)?
Correct answer: A
Slope = −7 − 54 − (−2) = −126 = −2. Dividing the change in x by the change in y gives −12.
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Question 2
Which equation describes the line with slope 3 that passes through (2, −1)?
Correct answer: A
Point-slope form: y + 1 = 3(x − 2), so y = 3x − 6 − 1 = 3x − 7. Check: 3(2) − 7 = −1.
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Question 3
The graph of a linear function is shown.
Which equation represents the line?
Correct answer: D
The line crosses the y-axis at (0, −1) and passes through (2, 3), so the slope is 3 − (−1)2 − 0 = 2. The equation is y = 2x − 1.
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Question 4
Which line is parallel to 4x − 2y = 6 and passes through (1, 5)?
Correct answer: C
Solving 4x − 2y = 6 for y gives y = 2x − 3, so the slope is 2. A parallel line through (1, 5): y − 5 = 2(x − 1), so y = 2x + 3. The line y = 2x − 3 is the original line itself, which does not pass through (1, 5).
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Question 5
What is the slope of a line perpendicular to y = 34x − 2?
Correct answer: A
Perpendicular slopes are negative reciprocals: the reciprocal of 34 is 43, and the sign changes, giving −43.
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Question 6
What is the x-intercept of the line 3x − 5y = 15?
Correct answer: D
At the x-intercept y = 0, so 3x = 15 and x = 5. The point (0, −3) is the y-intercept.
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Question 7
x 0 2 4 6 y 7 4 1 −2 Which linear function fits the table?
Correct answer: C
Each time x increases by 2, y decreases by 3, so the slope is −32. At x = 0, y = 7. The slope −3 uses the change in y per step without dividing by 2.
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Question 8
If f(x) = −4x + 9, for what value of x is f(x) = −11?
Correct answer: B
Set −4x + 9 = −11: −4x = −20, so x = 5. The value 53 is f(−11), which answers a different question.
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Question 9
A candle is 30 cm tall and burns down at a constant rate of 2.5 cm per hour. After how many hours will it be 10 cm tall?
Correct answer: B
The height is h(t) = 30 − 2.5t. Solve 30 − 2.5t = 10: 2.5t = 20, so t = 8. The answer 12 is how long the whole candle lasts.
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Question 10
A plumber's total charge in dollars for a job of h hours is C = 45h + 60. What does the number 60 represent?
Correct answer: B
When h = 0, C = 60, so 60 is the starting fee (the y-intercept). The hourly rate is 45, and a one-hour job costs 45 + 60 = 105.
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Question 11
What are the slope and y-intercept of the line 2x + 3y = 12?
Correct answer: C
Solve for y: 3y = −2x + 12, so y = −23x + 4. Both terms must be divided by 3, which is why the intercept is 4, not 12.
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Question 12
Which point lies on the line y = −2x + 5?
Correct answer: D
Substitute x = 3: −2(3) + 5 = −1, which matches. For (−1, 3) the line gives y = 7, and for (2, 2) it gives y = 1.
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Question 13
Which equation describes the line through (3, −4) and (3, 6)?
Correct answer: A
Both points have x = 3, so the line is vertical and every point on it has x = 3. Its slope is undefined. y = 3 would be a horizontal line.
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Question 14
Which set of ordered pairs represents a function?
Correct answer: B
In a function each input has exactly one output. In {(1, 4), (2, 4), (3, 4)} every x appears once; repeated outputs are allowed. The other sets repeat an input (2, 0 or 5) with different outputs.
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Question 15
A line passes through (2, k) and (6, 11) and has slope 32. What is the value of k?
Correct answer: C
Slope: 11 − k6 − 2 = 32, so 11 − k = 6 and k = 5. Subtracting in the wrong order (k − 11 = 6) gives 17.
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