Graphing the Equation y = 1/3x - 2

Introduction

• Discussed the equation in slope-intercept form: ( y = mx + b ).
• ( m ) represents the slope and ( b ) represents the y-intercept.

Identifying Parameters

• For the equation ( y = \frac{1}{3}x - 2 ):
  • Slope (m): ( \frac{1}{3} ).
  • Y-intercept (b): ( -2 ).

Understanding the Y-intercept

• Y-intercept is where the line crosses the y-axis, which occurs when ( x = 0 ).
• Calculation: Set ( x = 0 ), then ( y = -2 ).
• The point ( (0, -2) ) is on the graph.

Understanding the Slope

• Slope (m) tells us the ratio of change in ( y ) to the change in ( x ).
• Slope ( \frac{1}{3} ) means for every increase of 3 in ( x ), ( y ) increases by 1.

Graphing Steps

1. Plot the y-intercept:
   • Start at ( (0, -2) ).
2. Use the slope to find more points:
   • Move 3 units right (increase ( x ) by 3), then 1 unit up (increase ( y ) by 1); point is ( (3, -1) ).
   • Repeat to find points: If ( x ) decreases by 3, ( y ) decreases by 1.
   • Example points:
     • ( (3, -1) ), ( (-3, -3) ), ( (6, 0) ), etc.
3. Draw the line:
   • Connect the points to form a straight line representing the equation.

Conclusion

• Successfully graphed the line for the equation ( y = \frac{1}{3}x - 2 ) using slope-intercept form.
• The graph is a visual representation of how ( y ) changes with ( x ), maintaining the given slope and y-intercept.