Calculating Slope in Linear Functions
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Questions and Answers

What is the slope of the line that passes through the points (0, -2) and (3, 4)?

  • -2
  • 2 (correct)
  • 1.5
  • 3
  • If the cost of candy is $3 for every ounce, what is the rate of change represented by the slope?

  • $2 for every ounce
  • $0.50 for every ounce
  • $3 for every ounce (correct)
  • $1.00 for every ounce
  • Using the points (-4, -4) and (8, 4), what is the calculated slope of the line?

  • 3/4
  • 2/3 (correct)
  • 1/2
  • 5/6
  • If the slope indicates that a candle burns down at a rate of 2/3 inches for every 12 minutes, how many inches does it burn down in 10 minutes?

    <p>0.67 inches</p> Signup and view all the answers

    What is the overall implication when a slope of 3 is derived from a graph that depicts cost per ounce of candy?

    <p>The candy price increases by $3 for every ounce sold.</p> Signup and view all the answers

    Study Notes

    Slope Calculation for Lines

    • Slope represents the rate of change in a line graph, calculated using the formula m = (y2 - y1) / (x2 - x1).
    • For a line through points (0, -2) and (3, 4):
      • y2 = 4 and y1 = -2
      • x2 = 3 and x1 = 0
      • Calculation yields a slope of m = (4 - (-2)) / (3 - 0) = 6 / 3 = 2.

    Cost of Candy as a Function

    • The graph illustrates the cost of candy per ounce, with several potential rates:
      • 3,3, 3,0.38, 2.66,and2.66, and 2.66,and0.50 per ounce.
    • Slope provides insight into the price increase relative to weight.

    Candle Burning Rate

    • The graph tracks candle height (y) against time in minutes (x).
    • Selected points (-4, -4) and (8, 4):
      • y2 = 4 and y1 = -4
      • x2 = 8 and x1 = -4
      • Slope calculation: m = (4 - (-4)) / (8 - (-4)) results in m = 8 / 12 = 2 / 3.
    • Equivalent to a burning rate of 1 inch every 10 minutes, indicating the time taken for height reduction.

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    Description

    This quiz covers the calculation of slope using various examples, including a line graph, cost of candy, and the burning rate of a candle. Participants will learn how to apply the slope formula to different scenarios. Test your understanding of linear relationships and their graphical representation!

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