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  • 1. 2.3 LINEAR FUNCTIONS AND SLOPE-INTERCEPT FORM 2.4 MORE ABOUT LINEAR EQUATIONS
  • 2. LINEAR FUNCTIONS
    • A linear function is a function whose graph is a line.
    • We represent a linear function with a linear equation .
  • 3. INTERCEPTS
    • An intercept of a line is a point where a line crosses an axis.
      • The y-intercept is the point at which the line crosses the y-axis.
      • The x-intercept is the point at which the line crosses the x-axis.
  • 4. TO FIND THE INTERCEPTS
    • Set x = 0 and solve for y
    • Set y = 0 and solve for x
    • List your solutions as ordered pairs
  • 5. EXAMPLE: WHAT ARE THE INTERCEPTS OF THE EQUATION?
  • 6. SLOPE – INTERCEPT FORM The slope-intercept of an equation of a line is y = mx + b , where m is the slope of the line and (0, b ) is the y -intercept.
  • 7. EXAMPLE: WHAT IS AN EQUATION OF THE LINE
    • and the y-intercept is
  • 8. EXAMPLE: WHAT IS AN EQUATION OF THE LINE
  • 9. WORKING WITH LINEAR EQUATIONS
    • We can rewrite a linear equation in slope – intercept form by solving for y.
  • 10. EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.
  • 11. EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.
  • 12. POINT – SLOPE FORM
    • Given a point and the slope of a line we can write the equation of the line in point – slope form
  • 13. EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE
    • A line passes through with slope
    • What is an equation of the line?
  • 14. EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE
    • A line passes through with slope
    • What is an equation of the line?
  • 15. WRITING AN EQUATION GIVEN TWO POINTS
    • Find the slope
    • Substitute the slope and either point into the point-slope form
  • 16. EXAMPLE
    • A line passes through (3, 2) and (5, 8). What is an equation of the line in point-slope form?
  • 17. STANDARD FORM
    • Another form of the equation of a line is standard form .
      • The coefficients of x and y and the constant should be intgers
      • A should be postive!
  • 18. WRITING AN EQUATION IN STANDARD FORM WITH INTEGER COEFFICIENTS
    • Isolate the constant
    • Eliminate Fractions:
    • Multiply each side of the equation by the least common denominator of all fraction coefficients
  • 19. EXAMPLE: WRITE THE EQUATION IN STANDARD FORM.
  • 20.