Slope Review in Algebra

Introduction to Slope

• Definition: The slope of a line measures its steepness and is calculated as "rise over run" (change in y divided by change in x).
• Mathematical Formula:
  • Slope = (\frac{\Delta y}{\Delta x})

Key Concepts

Slope from a Graph

• Example: Given a line that intersects points (0,5) and (4,2):

  • Change in y (rise): (5 - 2 = 3)
  • Change in x (run): (4 - 0 = 4)
  • Slope = (\frac{3}{-4})

• Interpretation: For every 3 units moved vertically down, move 4 units horizontally to the right.

Slope from Two Points

• Example: Find slope from points (11.4,11.5) and (12.7,15.4):
  • Change in y: (15.4 - 11.5 = 3.9)
  • Change in x: (12.7 - 11.4 = 1.3)
  • Slope = (\frac{3.9}{1.3} = 3)

Practice Problems

• Problem: Determine the slope of a line intersecting points (1,2) and (4,4).
  • Calculate rise and run to find slope = (\frac{2}{3}).

Discussion and Questions

• Why use y/x for slope: It's a measure of how fast the line rises/falls (steepness), not side-to-side motion.
• Slope from Equations: In a linear equation (y=mx+b), the slope is "m".
• Slope as a Fraction: Always expressed as rise over run, even if the value is a whole number (5 becomes (\frac{5}{1})).

Additional Resources

• Videos:
  • Introduction to Slope
  • Finding Slope from a Graph
  • Finding Slope from Two Points
• Exercises:
  • Practice slope from graphs
  • Practice slope from points

Tips for Understanding Slope

• Use exact points for calculations to ensure accuracy.
• Recognize the importance of coordinates where the graph intersects grid lines.