Finding Slope and Y-Intercept from Linear Equations

Introduction

• Slope-Intercept Form: General form is ( y = mx + b )
  • ( m ): slope (coefficient of ( x ))
  • ( b ): y-intercept (constant term)

Simple Example

• Equation: ( y = 2x + 3 )
  • Slope (( m )): 2
  • Y-intercept (( b )): 3

Examples

1. Example 1: ( y = \frac{3}{4}x - 5 )

   • Slope: ( \frac{3}{4} )
   • Y-intercept: (-5)

2. Example 2: ( y = 8 - 4x )

   • Rewrite as: ( y = -4x + 8 )
   • Slope: (-4)
   • Y-intercept: 8

3. Example 3: ( y = 5 - x )

   • Rewrite as: ( y = -1x + 5 )
   • Slope: (-1)
   • Y-intercept: 5

4. Example 4: ( y = -7x )

   • Rewrite as: ( y = -7x + 0 )
   • Slope: (-7)
   • Y-intercept: 0

Special Cases

• Horizontal Line: ( y = c )

  • Slope: 0
  • Y-intercept: ( c )

• Vertical Line: ( x = c )

  • Slope: Undefined
  • Y-intercept: None

Additional Examples

1. Example 5: Convert standard form to slope-intercept form

   • Initial form: ( 3x - 5y = 8 )
   • Solve for ( y ):
     • Divide by coefficient of ( y )
     • Rearrange: ( y = \frac{3}{5}x - \frac{8}{5} )
     • Slope: ( \frac{3}{5} )
     • Y-intercept: (-\frac{8}{5})

2. Example 6: ( -\frac{2}{7}x + \frac{3}{7}y = \frac{4}{7} )

   • Multiply entire equation by 7 to eliminate fractions
   • Solve for ( y ):
     • Final form: ( y = \frac{2}{3}x + \frac{4}{3} )
     • Slope: ( \frac{2}{3} )
     • Y-intercept: ( \frac{4}{3} )

Conclusion

• Convert to Slope-Intercept Form: Always rearrange the equation to ( y = mx + b ) to find slope and y-intercept.
• Special Lines: Horizontal lines (slope = 0) and vertical lines (undefined slope) have unique characteristics.

Resources

• Additional content and resources are available in video description and related links.
  • Check out video-tutor.net for more tutorials and exam preparation.

End of Notes