GED Math Practice Test: Linear Functions, Slope and Graphs
- Linear Functions, Slope and Graphs
- 10 questions
- 15 minutes
These questions cover slope, intercepts, function notation and writing linear equations from words or tables. Before you pick an equation, test it with one point you already know.
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 that passes through the points (2, 5) and (6, 13)?
Correct answer: B
Slope is the change in y divided by the change in x: (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2. The answer 1/2 divides the change in x by the change in y.
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Question 2
At which point does the graph of y = −3x + 7 cross the y-axis?
Correct answer: D
A graph crosses the y-axis where x = 0, and then y = −3(0) + 7 = 7. The number −3 is the slope, not the intercept.
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Question 3
If f(x) = 4x − 9, what is f(−2)?
Correct answer: A
Replace x with −2: 4(−2) − 9 = −8 − 9 = −17. The answer −1 comes from treating 4(−2) as +8.
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Question 4
Which equation describes the line with slope 3 that passes through the point (1, 4)?
Correct answer: C
Use y = 3x + b with the point (1, 4): 4 = 3(1) + b, so b = 1. The line y = 3x + 4 has the right slope but passes through (0, 4), not (1, 4).
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Question 5
A plumber charges a $65 service fee for each visit plus $48 for each hour of work. Which function gives the total charge C, in dollars, for a visit that lasts h hours?
Correct answer: B
The hourly rate is multiplied by the number of hours, and the one-time fee is added once: C = 48h + 65. The function C = 65h + 48 charges the visit fee for every hour.
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Question 6
Line k has the equation y = 2x − 5. What is the slope of a line perpendicular to line k?
Correct answer: C
Perpendicular slopes are negative reciprocals, and the negative reciprocal of 2 is −1/2. A slope of 2 would make the lines parallel.
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Question 7
x 0 1 2 3 y 5 8 11 14 Which equation fits every pair of values in the table?
Correct answer: D
Each time x goes up by 1, y goes up by 3, so the slope is 3; when x = 0, y = 5. The equation y = 5x + 3 swaps the slope and the intercept and gives 3 when x = 0.
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Question 8
At what point does the graph of 2x + 5y = 20 cross the x-axis?
Correct answer: A
On the x-axis y = 0, so 2x = 20 and x = 10. The point (0, 4) is where the line crosses the y-axis.
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Question 9
A tank holds 600 gallons of water. A valve is opened, and the water drains at a steady rate of 25 gallons per minute. The amount left after t minutes is W = 600 − 25t. After how many minutes is the tank empty?
Correct answer: B
The tank is empty when W = 0: 600 − 25t = 0, so t = 600 ÷ 25 = 24. Choosing 25 confuses the rate with the time.
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Question 10
Which point lies on the line y = −2x + 3?
Correct answer: C
For x = 4, y = −2(4) + 3 = −8 + 3 = −5, so (4, −5) is on the line. For (2, 1), the equation gives y = −1, not 1.
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