Calculating Slope from Points and Tables

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.