Grade 8 Math Practice Test: Writing Linear Functions from Words, Tables and Two Points
- Writing Linear Function Models
- 10 questions
- 15 minutes
This test covers building a linear function y = mx + b from a situation, a table or two data points, and explaining what the rate of change m and the initial value b mean. Tip: find m from two points first, then work backward to x = 0 to get b.
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Question 1
A tank drains at a constant rate. After 2 minutes it holds 46 gallons, and after 5 minutes it holds 37 gallons. Which function gives the gallons g after t minutes?
Correct answer: B
Rate of change = (37 − 46) ÷ (5 − 2) = −3 gallons per minute. Going back 2 minutes from 46 gives 46 + 6 = 52 at t = 0. g = −3t + 46 uses the value at t = 2 as if it were the start.
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Question 2
The tank in the previous question follows g = −3t + 52. What does 52 represent?
Correct answer: D
52 is the value of g when t = 0, so it is the starting amount. The amount that drains each minute is the rate 3, and the gallons after 2 minutes is 46.
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Question 3
The table shows a linear function.
x 3 6 9 y 20 32 44 Which equation represents the function?
Correct answer: C
When x increases by 3, y increases by 12, so m = 12 ÷ 3 = 4. Then 20 = 4 · 3 + b gives b = 8. y = 12x + 20 uses the change in y as the slope and the first y-value as the intercept.
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Question 4
A repair shop charges a fixed fee plus an hourly rate. A 2-hour repair costs $95, and a 4-hour repair costs $155. What is the fixed fee?
Correct answer: D
Two extra hours cost $60, so the rate is $30 per hour. A 2-hour repair includes $60 of labor, so the fixed fee is $95 − $60 = $35. $30 is the hourly rate, and $47.50 is just 95 ÷ 2.
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Question 5
A gift card starts with $300. Ava spends the same amount each week, and after 6 weeks the card is empty. Which function gives the balance y after x weeks?
Correct answer: C
The line passes through (0, 300) and (6, 0), so m = −300 ÷ 6 = −50 and b = 300. y = 50x + 300 would make the balance grow.
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Question 6
The temperature of an oven, in °F, t minutes after it is turned on is T = 25t + 70, until it reaches the set temperature. What does 25 represent?
Correct answer: B
25 is the coefficient of t, the rate of change: each minute adds 25°F. The starting temperature is the constant 70°F.
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Question 7
An elevator starts 120 feet above the ground and goes down at a steady 8 feet per second. After how many seconds is it 24 feet above the ground?
Correct answer: A
Its height is h = 120 − 8t. Set 120 − 8t = 24: 8t = 96, so t = 12 seconds. 15 seconds is the time to reach the ground (120 ÷ 8).
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Question 8
A candle burns at a steady rate. After 3 hours of burning it is 21 cm tall, and after 7 hours it is 13 cm tall. How tall was the candle before it was lit?
Correct answer: D
It loses (21 − 13) ÷ (7 − 3) = 2 cm per hour. Going back 3 hours from 21 cm adds 6 cm, so it started at 27 cm. 21 cm is the height after 3 hours, not at the start.
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Question 9
Which situation can be modeled by y = 12x + 30?
Correct answer: A
In y = mx + b, the rate m = 12 is the amount per session and b = 30 is the one-time starting amount. Spending $12 each week would need a slope of −12.
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Question 10
A car starts with 14 gallons of gas and uses 1 gallon every 28 miles. Which function gives the gallons g left after m miles?
Correct answer: A
The car uses 1/28 gallon per mile, so the rate of change is −1/28 and the starting value is 14. g = 14 − 28m would use 28 gallons per mile.
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