Grade 8 Math Practice Test: Linear Equations and Functions
- Linear Equations and Functions
- 12 questions
- 15 minutes
This test covers solving linear equations, slope, writing equations in the form y = mx + b and reading functions from tables. Tip: slope is the change in y divided by the change in x, so subtract the coordinates in the same 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
Solve for x.
3x + 7 = 25
Correct answer: C
Subtract 7 from both sides: 3x = 18. Then divide both sides by 3: x = 6. x = 18 stops before the last step, and 323 adds 7 instead of subtracting it.
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Question 2
Solve for x.
5x − 4 = 2x + 11
Correct answer: B
Subtract 2x from both sides: 3x − 4 = 11. Add 4 to both sides: 3x = 15, so x = 5. 157 comes from adding 2x to the left side instead of subtracting it.
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Question 3
Solve for x.
2(x − 3) + 4 = 3x − 5
Correct answer: A
Distribute: 2x − 6 + 4 = 3x − 5, so 2x − 2 = 3x − 5. Subtract 2x and add 5 to both sides: x = 3. x = 6 comes from multiplying only the x by 2 and writing 2x − 3.
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Question 4
How many solutions does this equation have?
4(x + 2) = 4x + 8
Correct answer: D
Distributing gives 4x + 8 = 4x + 8, which is true for every value of x, so there are infinitely many solutions. If the two sides had the same x-term but different constants, such as 4x + 8 = 4x + 5, there would be no solution.
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Question 5
What is the slope of the line that passes through the points (2, 5) and (6, 13)?
Correct answer: A
Slope = change in y ÷ change in x = (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2. 12 puts the change in x on top.
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Question 6
Which equation describes a line with a slope of 4 and a y-intercept of −3?
Correct answer: D
In y = mx + b, m is the slope and b is the y-intercept. With m = 4 and b = −3, the equation is y = 4x − 3. y = −3x + 4 swaps the slope and the intercept.
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Question 7
What are the slope and the y-intercept of the line y = −2x + 5?
Correct answer: C
In y = mx + b, the number multiplied by x is the slope and the constant is the y-intercept, so m = −2 and b = 5. Keep the sign that belongs to each number: the slope is negative, the intercept is positive.
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Question 8
The table shows a linear function.
x 0 1 2 3 y 4 7 10 13 Which equation represents the function?
Correct answer: B
y increases by 3 each time x increases by 1, so the slope is 3. When x = 0, y = 4, so the y-intercept is 4: y = 3x + 4. y = 4x + 3 swaps the two numbers.
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Question 9
Which set of ordered pairs is NOT a function?
Correct answer: D
In a function, each input (x-value) has exactly one output. The input 2 is paired with both 3 and 7, so that set is not a function. Repeated outputs, as in {(1, 5), (2, 5), (3, 5)}, are allowed.
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Question 10
A gym charges a $25 sign-up fee plus $15 per month. Which equation gives the total cost C, in dollars, after m months?
Correct answer: A
The monthly charge grows with m, so 15 is the rate of change; the one-time fee of 25 is the starting value. C = 25m + 15 would charge $25 every month.
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Question 11
A candle is 18 cm tall. It burns down 1.5 cm every hour. After how many hours will the candle be 6 cm tall?
Correct answer: B
The height after t hours is 18 − 1.5t. Set 18 − 1.5t = 6, so 1.5t = 12 and t = 8. 12 is the number of centimeters that burn away, not the number of hours.
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Question 12
Function A is y = 3x + 2. Function B is shown in the table.
x 0 2 4 y 1 9 17 Which statement is true?
Correct answer: C
The rate of change of function B is (9 − 1) ÷ (2 − 0) = 4, which is greater than the slope of function A, 3. The y-intercept of B is 1, which is less than the y-intercept of A, 2.
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