5 7 Standard Form

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5 7 Standard Form

  1. 1. Standard Form Ax + By = C Section 5.7
  2. 2. Standard form in General <ul><li>Standard form is tricky </li></ul><ul><li>Some textbooks will give you </li></ul><ul><ul><li>Ax + By = C </li></ul></ul><ul><li>Others will give you </li></ul><ul><ul><li>Ax + By + C = 0 </li></ul></ul><ul><li>Others may give you some slightly different variation </li></ul><ul><li>Focus on the A, B, C for Standard Form. </li></ul>
  3. 3. Ax + By = C <ul><li>A, B, C must be integers </li></ul><ul><li>A, B, C can NOT be decimals or fractions </li></ul><ul><li>Ax & By must be on the same side of the equation </li></ul><ul><li>It is preferred that A be positive (not necessary, but preferred) </li></ul><ul><li>That means that 4x - 3y = 6 is the same thing as -4x + 3y = -6 </li></ul>
  4. 4. Example 1- Find x & y intercepts of equations <ul><li>To find the x-intercept, replace y with 0 & solve for x. </li></ul><ul><li>To find the y-intercept, replace x with 0 & solve for y. </li></ul><ul><li>This works because: </li></ul><ul><ul><li>x-intercept is (x, 0) </li></ul></ul><ul><ul><li>y-intercept is (0,y) </li></ul></ul>
  5. 5. Example 1- Find x & y intercepts of equations <ul><li>You can use the x & y intercepts to graph. </li></ul><ul><li>Just plot the two intercepts and draw the line through the two points. </li></ul>
  6. 6. Example 2 - Graph equations in standard form <ul><li>Use inverse operations to move the equation into slope intercept form. </li></ul><ul><li>Change of instructions above problem 17 on the back: </li></ul><ul><li>Rewrite the equation to slope-intercept form </li></ul>
  7. 7. Example 3 - Word Problems <ul><li>We are going to do Example 4 before we do Example 3. </li></ul><ul><li>We’ll come back to Example 3. </li></ul>
  8. 8. Example 4 - Find Standard Form from a point and the slope <ul><li>You will be given a point & the slope </li></ul><ul><li>We found slope-intercept form from a point and the slope in lesson 5-5. </li></ul>
  9. 9. Example 4 - Find Standard Form from a point and the slope <ul><li>After you find slope intercept form: </li></ul><ul><li>Multiply the equation by an LCD to get rid of any denominators. </li></ul><ul><li>Use inverse operations to move any terms one at a time until the equation is in Ax + By = C form. </li></ul>
  10. 10. One Last Thing <ul><li>If you are given two points and told to put it in Standard Form: </li></ul><ul><li>Find the slope </li></ul><ul><li>Use the slope and one of the points to find slope-intercept form. </li></ul><ul><li>Then follow the instructions on the previous screen to move the equation into standard form. </li></ul>
  11. 11. Review <ul><li>What is Standard Form. </li></ul><ul><li>How do you find the x & y intercepts? </li></ul><ul><li>How do you use the intercepts to graph an equation? </li></ul><ul><li>How do you graph an equation from standard form? </li></ul>
  12. 12. Review <ul><li>What steps do you take to solve a word problem? </li></ul><ul><li>What steps do you take to write a standard form equation given a point and the slope? </li></ul><ul><li>What steps do you take to write a standard form equation given two points? </li></ul>

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