2.3 LINEAR FUNCTIONS AND SLOPE-INTERCEPT FORM 2.4 MORE ABOUT LINEAR EQUATIONS
LINEAR FUNCTIONS <ul><li>A  linear function  is a function whose graph is a line. </li></ul><ul><li>We represent a linear ...
INTERCEPTS <ul><li>An  intercept  of a line is a point where a line crosses an axis. </li></ul><ul><ul><li>The  y-intercep...
TO FIND THE INTERCEPTS <ul><li>Set x = 0 and solve for y </li></ul><ul><li>Set y = 0 and solve for x </li></ul><ul><li>Lis...
EXAMPLE: WHAT ARE THE INTERCEPTS OF THE EQUATION?
SLOPE – INTERCEPT FORM The  slope-intercept  of an equation of a line is  y = mx + b , where  m  is the slope of the line ...
EXAMPLE: WHAT IS AN EQUATION OF THE LINE <ul><li>and the y-intercept is  </li></ul>
EXAMPLE: WHAT IS AN EQUATION OF THE LINE
WORKING WITH LINEAR EQUATIONS <ul><li>We can rewrite a linear equation in slope – intercept form by solving for y. </li></ul>
EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.
EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.
POINT – SLOPE FORM <ul><li>Given a point    and the slope  of a line we can write the equation of the line in  point – slo...
EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE <ul><li>A line passes through with slope </li></ul><ul><li>What i...
EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE <ul><li>A line passes through with slope </li></ul><ul><li>What i...
WRITING AN EQUATION GIVEN TWO POINTS <ul><li>Find the slope </li></ul><ul><li>Substitute the slope and either point into t...
EXAMPLE <ul><li>A line passes through (3, 2) and (5, 8). What is an equation of the line in point-slope form? </li></ul>
STANDARD FORM <ul><li>Another form of the equation of a line is  standard form . </li></ul><ul><ul><li>The coefficients of...
WRITING AN EQUATION IN STANDARD FORM WITH INTEGER COEFFICIENTS <ul><li>Isolate the constant </li></ul><ul><li>Eliminate Fr...
EXAMPLE: WRITE THE EQUATION IN STANDARD FORM.
 
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2.3 and 2.4 Lines

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2.3 and 2.4 Lines

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

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