Linear Functions Quiz
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Linear Functions Quiz

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@LowRiskArithmetic

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Questions and Answers

What does the number 45 represent in the context of Marisol's journey from City A to City B?

  • Marisol took 45 trips from City A to City B.
  • The distance between City A and City B is 45 miles.
  • Marisol drove at an average speed of about 45 miles per hour. (correct)
  • It took Marisol 45 hours to drive from City A to City B.

    • If Marisol drove for 3 hours at an average speed of 45 miles per hour, how far did she travel?

  • 180 miles (correct)
  • 135 miles
  • 150 miles
  • 90 miles

    • What is the value of speed in miles per hour of the car 5 seconds after it started accelerating, according to the given equation?

  • 60 miles per hour
  • 40 miles per hour
  • 45 miles per hour
  • 55 miles per hour (correct)

    • If a car's speed is represented as a function of time in seconds, which of the following correctly describes the relationship?

    <p>Speed increases as time increases.</p> Signup and view all the answers

    If Marisol drove for t hours, how would you represent the distance she traveled mathematically?

    <p>d = 45t</p> Signup and view all the answers

    When calculating Marisol's distance, which of these aspects must be considered?

    <p>The speed maintained during the trip.</p> Signup and view all the answers

    How many total miles would be traveled if the car accelerates to 55 miles per hour over a period of time?

    <p>Cannot be determined without time.</p> Signup and view all the answers

    What would be an incorrect assumption about the car's speed recorded after it began accelerating?

    <p>The speed can immediately be considered constant.</p> Signup and view all the answers

    What does T represent in the equation for Brittany's total take-home pay?

    <p>Total take-home pay in dollars</p> Signup and view all the answers

    If Brittany's total take-home pay was $1,576, what was the equation used to determine the number of hours she worked?

    <p>$1,576 = 18h + 1,000$</p> Signup and view all the answers

    How many hours did Brittany work to achieve a total pay of $1,576?

    <p>32</p> Signup and view all the answers

    What is the value of the constant a in the function g(x) = 5x + a if g(4) = 31?

    <p>11</p> Signup and view all the answers

    What value is obtained by substituting x = 9 into the equation f(x) = 100x + 2?

    <p>902</p> Signup and view all the answers

    If Brittany's pay was calculated based on 18 dollars per hour, what was her hourly wage based on her total pay?

    <p>$18</p> Signup and view all the answers

    Which operation would you perform first to solve for h in the equation $1,576 = 18h + 1,000$?

    <p>Subtract 1,000 from both sides</p> Signup and view all the answers

    If the sign-on bonus is $1,000 and the total pay is $1,576, how much of that pay was from hourly wages?

    <p>$576</p> Signup and view all the answers

    What will be the distance of the bus from the marker 2 seconds after passing it?

    <p>60 feet</p> Signup and view all the answers

    Which of the following describes the cost for making a specific number of rings according to the line shown?

    <p>The cost increases linearly with an increase in the number of rings.</p> Signup and view all the answers

    What does the y-coordinate of the point on the line represent when the x-coordinate is 60?

    <p>The total cost in dollars for making 60 rings</p> Signup and view all the answers

    What is a common error that might lead to selecting the wrong option for the bus distance 2 seconds after passing the marker?

    <p>Forgetting to multiply the coefficient properly</p> Signup and view all the answers

    If a manufacturer wants to produce 100 rings, what information does the y-coordinate provide?

    <p>It determines the total cost for making 100 rings</p> Signup and view all the answers

    If the bus travels at a constant speed of 30 feet per second, how far will it travel in 5 seconds?

    <p>120 feet</p> Signup and view all the answers

    What is the correct interpretation of the slope in the cost versus number of rings graph?

    <p>The cost per ring produced</p> Signup and view all the answers

    Which of the following distances will the bus NOT be after 1 second according to the equation $d = 30t$?

    <p>60 feet</p> Signup and view all the answers

    What is the function that models the number of minutes it will take Juan to ride $x$ miles at his average rate of 5.7 minutes per mile?

    <p>$m(x) = 5.7x$</p> Signup and view all the answers

    Given that the graph of $y = f(x)$ has a slope of 3 and passes through the point (0, -8), what is the y-intercept of the graph?

    <p>-8</p> Signup and view all the answers

    What is the general form of the equation for a linear function given a slope of $m$ and a y-intercept of $b$?

    <p>$f(x) = mx + b$</p> Signup and view all the answers

    If Juan doubles the distance he rides, how will his total time in minutes change?

    <p>11.4</p> Signup and view all the answers

    What would be the equation of a line with a slope of 3 that passes through the point (1, -5)?

    <p>$f(x) = 3x - 2$</p> Signup and view all the answers

    If the average rate at which Juan bikes were halved to 2.85 minutes per mile, how many minutes would it take him to bike 4 miles?

    <p>7.14</p> Signup and view all the answers

    Which of the following statements about linear functions is false?

    <p>A linear function's graph is always a curved line.</p> Signup and view all the answers

    What is the value of the slope in the equation $f(x) = 3x - 8$?

    <p>3</p> Signup and view all the answers

    If Robert rented a truck and was charged an initial fee of $20.00 plus $0.70 per mile, what will be the total cost if he drove 60 miles?

    <p>$62.00</p> Signup and view all the answers

    What is the correct representation of the total charge Robert incurred if he drove $m$ miles?

    <p>$20 + 0.70m$</p> Signup and view all the answers

    How many miles does Robert need to drive for the total cost to equal $46.60?

    <p>38 miles</p> Signup and view all the answers

    What does the equation representing the snow leopard population indicate when $t = 30$?

    <p>The year 2020</p> Signup and view all the answers

    Which answer choice correctly interprets the snow leopard population equation for the year 2030?

    <p>The population will be 550.</p> Signup and view all the answers

    If the snow leopard population is represented as $P(t)$, what does $P(30)$ equal?

    <p>550</p> Signup and view all the answers

    What may cause a student to incorrectly conclude that the population is 30 in the year 2030?

    <p>Confusing years with different values of $t$.</p> Signup and view all the answers

    What is the total amount Robert was charged if he drove 50 miles?

    <p>$55.00</p> Signup and view all the answers

    Study Notes

    Linear Functions

    • In the equation d = 30t, d represents the distance in feet from a road marker that a bus will be t seconds after passing the marker.
    • When t = 2, the bus will be 60 feet from the marker.
    • The equation y = 175 represents the cost (y) in dollars for a manufacturer to make x rings.
    • When x = 60, the cost is $175.
    • Juan's biking:
      • He rides at an average rate of 5.7 minutes per mile.
      • The function mx = 5.7x models the time in minutes (mx) it will take Juan to ride x miles.
    • The function f(x) = 3x - 8 defines a linear function with a slope of 3 and a y-intercept of (0, -8).
    • Marisol's trip:
      • The equation d = 45t estimates the distance d (in miles) Marisol travels after t hours.
      • 45 represents her average speed of 45 miles per hour.
    • The equation s = 40 + 35t gives the speed s (in miles per hour) of a car t seconds after it begins to accelerate.
    • When t = 5, the car's speed is 55 miles per hour.
    • Brittany's pay:
      • The equation T = 18h + 1000 represents her total take-home pay (T) for her first week, where h is the number of hours worked.
      • When T = 1576, Brittany was paid for 32 hours.
    • The function g(x) = 5x + a is defined with a as a constant; g(4) = 31.
    • Therefore, a = 11.
    • The function f(x) = 100x + 2 is defined.
    • When x = 9, f(x) = 902.
    • Snow Leopard Population
      • The function P(t) = -2t + 550 models the population of snow leopards in a certain area, with t representing years after 1990.
      • The equation P(30) = 550 means that the snow leopard population is predicted to be 550 in the year 2020.

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    Description

    Test your understanding of linear functions through various real-world applications. This quiz covers concepts like distance, cost, speed, and time modeled by linear equations. Challenge yourself to solve problems based on the equations discussed.

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