Calculating Slope from Points and Tables
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Questions and Answers

What is the slope when given the points (0, -2) and (3, 4)?

  • 1
  • 2 (correct)
  • 4
  • 3
  • Using the ski rental package table, what is the cost per additional person?

  • $30
  • $50
  • $40 (correct)
  • $20
  • What is the slope derived from the time and distance table?

  • $102$ miles per hour
  • $408$ miles per hour
  • $51$ miles per hour (correct)
  • $204$ miles per hour
  • Calculate the slope between the points (10, -1) and (-8, 6).

    <p>$-\frac{1}{6}$</p> Signup and view all the answers

    From the ski rental package table, what is the total cost for 4 people?

    <p>$160</p> Signup and view all the answers

    Study Notes

    Calculating Slope from Points and Tables

    • Slope formula: (m = \frac{y_2 - y_1}{x_2 - x_1}) calculates the rate of change between two points.
    • For points (0, -2) and (3, 4):
      • (m = \frac{4 - (-2)}{3 - 0} = \frac{6}{3} = 2), indicating a positive slope.
    • Selecting points from a table follows the same process; the slope remains consistent regardless of the source (points or tables).

    Slope Example from Given Points

    • To find the slope for points (10, -1) and (-8, 6):
      • Calculate using the formula:
      • (m = \frac{6 - (-1)}{-8 - 10} = \frac{7}{-18} = -\frac{1}{6}).

    Cost per Person in a Rental Package

    • A table shows costs for a ski rental package:
      • Cost increases consistently at $40 per additional person.
      • At 4 people, the total cost is $160, equating to $40 per person.
      • Slope: (m = \frac{1}{40}) dollars per room, with each person's cost being $40.

    Distance Travelled Over Time

    • Another table outlines distance driven over specified times:
      • Incrementally, distance rises by 102 miles every 2 hours.
      • This translates to a rate of 51 miles per hour, derived from (m = \frac{102}{2} = 51).

    Key Definitions

    • Slope: Represents the steepness or incline of a line, indicating how much y changes for a unit change in x.
    • Linear relationship: Demonstrated through consistent rates of change in data tables.

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    Description

    This quiz explores how to calculate the slope of a line given two points or a set of values in a table. You'll learn to use the slope formula effectively and apply it in different scenarios. Test your understanding with various question types to solidify your knowledge.

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