Rewriting Linear Equation from standard form to slope intercept form
- 1. Submitted by: JANET J. ELAD Teacher III STRATEGIC INTERVENTION MATERIAL IN MATHEMATICS VIII (FIRST QUARTER) Checked by: ASUNCION A. EALA Principal I
- 2. GUIDE CARD Lesson Essential Question: How doyou rewriteequations from standard form tographing form? Standard Form Slope-Intercept Form Ax +By=C y=mx +b
- 3. Forms of Linear Equations • The forms oflinearequationsare the formatsin whichthe informationis writtenin. • These two forms are the most commonly used ways to write linearequations. 1. StandardForm: Ax + By =C 2. SlopeIntercept Form: y=mx+b
- 4. What is StandardForm ? • Standard Form is Ax + By = C • Basically, if your x and y are on thesame side of the equation,thenit is in standard form. Slope– Intercept Form y = mx + b m represents the slope b represents they-intercept What is Slope- Intercept Form ?
- 5. 3 Powerful Movesto get your equationinto y= mx +b 1. MOVE X 2. DROP ALL 3. dIVIDE ALL
- 6. 1. MOVE X Add or Subtract the x term to the other side of equals. Example# 1 write 6x + 4y = 12 intoy= mx + b 2. DROP ALL Bring all terms down in order. Do not add or subtract unlike terms!!! 6x + 4y = 12 -6x = -6x 4y = – 6x + 12 6x + 4y = 12 -6x = -6x
- 7. 3. DIVIDE ALL Divide each term by the number attached to y keep slope a fraction! 4y = -6x + 12 4y = – 6x + 12 4 4 4 y = – 3x + 3 2
- 8. 1. MOVE X Example# 2 write -4x +3y =12 into y= mx +b 2. DROP ALL -4x + 3y = 12 4x = 4x 3y = 4x + 12 -4x + 3y = 12 4x = 4x
- 9. 3. DIVIDE ALL 3y = 4x + 12 3y = 4x + 12 3 3 3 y = 4x + 4 3 3 Powerful Moves to write -4x + 3y =12 intoy= mx + b
- 10. 1. MOVE X 2. DROP ALL 9x - y = -8 -9x = -9x -y = -9x - 8 9x - y = -8 -9x = -9x Example# 3 Write 9x -y =-8 intoy= mx +b
- 11. 3. DIVIDE ALL - y = -9x - 8 -y = -9x - 8 -1 -1 -1 y = 9x + 8 3 Powerful Moves to write 9x -y =-8 intoy= mx + b
- 12. 1. MOVE X Example #4 Write -8x -4y = -16 intoy= mx +b 2. DROP ALL -8x - 4y = -16 8x = 8x -4y = 8x - 16 -8x - 4y = -16 8x = 8x
- 13. 3. DIVIDE ALL - 4y = 8x - 16 -4y = 8x - 16 -4 -4 -4 y = -2x + 4 3 Powerful Moves to write -8x - 4y =-16 intoy= mx + b
- 14. 1. MOVE X Example# 5 Write 3x +2y - 6 = 18 intoy= mx + b 2. DROP ALL 3x + 2y -6 = 18 -3x +6 = -3x + 6 2y = -3x + 24 3x + 2y - 6 = 18 -3x +6 = -3x + 6
- 15. 3. DIVIDE ALL 2y = -3x + 24 2y = -3x + 24 2 2 2 y = -3x + 12 2 Write 3x + 2y = 18 intoy= mx + b
- 16. 1.MOVE Example #6 Write -7x +14y + 3 = 3x + 31 into y= mx +b 2. DROP ALL -7x + 14y + 3 = 3x +31 7x - 3 = 7x -3 14y = 10x + 28 -7x + 14y + 3 = 3x + 31 7x - 3 = 7x - 3
- 17. 3. DIVIDE ALL 14y = 10x + 28 14y = 10x + 28 14 14 14 y = 5x + 2 7 Writing -7x + 14y = 28 into y=mx + b
- 18. 1. MOVE X Example #7 Write -5x + 3y =2y - 9 into y=mx +b 2. DROP ALL -5x + 3y = 2y -9 5x –2y = -2y +5x y = 5x - 9 -5x + 3y = 2y -9 5x -2y = -2y + 5x
- 19. Error Analysis JARED 12x + 3y = 9 3y = 9 – 12x y = 3 – 4x Ali 12x + 3y = 9 4x + y = 3 y = -4x + 3 Four students rewrote the equation 12x + 3y = 9 into slope-intercept form. Determine who did it correctly. If the student did it incorrectly, explainthe mistake. Molly 12x + 3y = 9 3y = 9 – 12x y = 3 – 12x Mia 12x + 3y = 9 3y = 9 – 12x y = 3 – 4x y = 4x - 3 ACTIVITY CARD 1
- 20. Identifythe equations in standardform A. 2x – 4y = 6 B. y = 3x + 1 C. x – y = 1 D. 4y = 5x + 8 E. -x + 2y = 6 F. y = 1/3x + 2.5 G. 2y +7 = 3x ACTIVITY CARD 2
- 21. ACTIVITY CARD 3
- 22. What is the country’s largest lake? ASSESSMENT CARD Rewrite the following equation into slope – intercept form. Notice the letter next to it. Write this letter next to each box containing the answerto each equation. G 15y = 30x L 64y = 4x B x = 3y +9 E x + 4y – 16 = 0 M 5x = y + 10 U 7x - 7y + 28 = 0 D 2x + y = 5 N 6x - 2y = 8 A x + y - 2 = 0
- 23. What is the country’s largest lake? y = 1/16x y = -x + 2 y = 2x y = x + 4 y = 3x - 4 y = -x + 2 y = -2x + 5 y = -x/ 4 + 4 y = x/ 3 - 3 y = -x +2 y = 6x + 1/ 2 ASSESSMENT CARD Write the letter of your answer next to each box containing each equation.
- 24. ASSESSMENT CARD Who was the Greek Mathematician considered as Father of Algebra?
- 25. ASSESSMENT CARD Write the letter of your answer next to each box containing each equation. Who wasthe Greek Mathematicianconsidered as Father of Algebra?
- 26. ENRICHMENT CARD
- 27. y = mx + b O y = 5x + 25 M y = -3x + 21 M x = 1/4y + 8 L x = -5/7y + 6 T y = 3/4x + 8 I y = 35 + 5x Z 5/6x + y = 1 E (y + 5)/(x – 6) = 1/5 N 3/5x = y + 12 N (3y + 2)/(x – 8) = 4 R 1/3x + 9y = 18 S y/2 = 3x + 3/5 D 2x – 8 = 3y + 6 U 1/2x – 4y = 16 A y/2 + x/3 = 1 ENRICHMENT CARD Kilometric distances are measured from what landmark in Transform the following equation into Standard form. Find the answer in the first table. Write in the second table the letter that corresponds to the correct answer.
- 28. LETTER ANSWER x + 27y = 54 5x – y = -35 5x + 6y = 6 2x + 3y = 6 7x + 5y = -42 4x + 2 = 2 3x + y = 21 5x – y = -25 4x – 3y = 34 x – 8y = 32 4x – y = 32 x – 5y = 31 3x – 5y = 60 3x – 4y = -32 ENRICHMENT CARD Kilometric distances are measured from what landmark in Transform the following equation into Standard form. Find the answer in the first table. Write in the second table the letter that corresponds to the correct answer.
- 29. Identifythe equations in standardform A. 2x – 4y = 6 C. x – y = 1 E. -x + 2y = 6 G. 2y +7 = 3x ANSWER CARD ACTIVITY # 1
- 30. 1. y = -2x + 9 m = -2 b = 9 2. y = -x/2 + 2 m = -1 b = 2 3. y = 3x -2 m = 3 b = -2 4. y = -5/2x + 7/2 m = -5/2 b = 7/2 5. y = x + 1/3 m = 1 b = 1/3 6. y = 5/7x – 2/7 m = 5/7 b = - 2/7 ANSWER CARDA C T I V I T Y # 2
- 31. What is the country’s largest lake? L y = 1/ 16x A y = -x + 2 G y = 2x U y = x + 4 N y = 3x - 4 A y = -x + 2 D y = -2x + 5 E y = -x/ 4 + 4 B y = x/ 3 - 3 A y = -x +2 Y y = 6x + 1/ 2 ANSWER TO ASSESSMENT CARD Write the letter of your answer next to each box containing each equation.
- 32. Write the letter of your answer next to each box containing each equation. D I O P H A N T U S ANSWER TO ASSESSMENT CARD Who wasthe Greek Mathematicianconsidered as Father of Algebra?
- 33. LETTER ANSWER r x + 27y = 54 i 5x – y = -35 z 5x + 6y = 6 a 2x + 3y = 6 l 7x + 5y = 42 4x + 2 = 2 m 3x + y = 21 O 5x – y = -25 n 4x – 3y = 34 u x – 8y = 32 m 4x – y = 32 e x – 5y = 31 n 3x – 5y = 60 t 3x – 4y = -32 Kilometric distances are measured from what landmark in Manila? ANSWER TO ENRICHMENT CARD
- 34. REFERENCE CARD Pathways to Mathematics I Merlinda M. Pata Page148 - 149 Pathways to Mathematics IV Merlinda M. Pata Page 32 www.Google.com