Key Concepts in Algebra 1

Key Concepts in Algebra 1

• Y-Intercept

  • Defined as the point where the graph intersects the y-axis, represented as (0, y).

• X-Intercept

  • Defined as the point where the graph intersects the x-axis, represented as (x, 0).

• Slope-Intercept Form

  • The general equation for linear functions, expressed as ( y = mx + b ) where:
    • ( m ) is the slope
    • ( b ) is the y-intercept

Slope of Lines

• For the equation ( y = x + 9 ):

  • The slope is represented as ( 1 ) (or ( 1x )).

• For the equation ( y = 5x - 7 ):

  • The slope is ( 5 ).

Writing Equations of Lines

• When given a slope of ( 5 ) and a y-intercept of (0, -7):

  • The equation is formulated as ( y = 5x - 7 ).

• For a line passing through the points (0, -6) and (4, 10):

  • The equation determined is ( y = 4x - 6 ).

Point-Slope Form

• To write the equation of a line using point-slope form passing through (7, 3) with a slope of ( 2 ):
  • The equation is ( y - 3 = 2(x - 7) ).

Intercepts of a Line

• For the line represented by ( 5x - 2y = 10 ):
  • The x-intercept is (2, 0), and the y-intercept is (0, -5).