Linear equations 2-3

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Linear equations 2-3

  1. 1. Graphs & Linear Equations Y X y=mx+b
  2. 2. Graphing Horizontal & Vertical Lines Y X x-axis y-axis This line has a y value of 4 for any x-value. It’s equation is y = 4 (meaning y always equals 4)
  3. 3. Graphing Horizontal & Vertical Lines Y X x-axis y-axis This line has a x value of 1 for any y-value. It’s equation is x = 1 (meaning x always equals 1)
  4. 4. The Equation of a Vertical Line is X=Constant Y X x-axis y-axis x = 1
  5. 5. The Equation of a Horizontal Line is Y=Constant Y X x-axis y-axis y = 3
  6. 6. Graph the following lines Y = -4 Y = 2 X = 5 X = -5 X = 0 Y = 0
  7. 7. Answers Y X x-axis y-axis x = 5 x = -5
  8. 8. Answers Y X x-axis y-axis y = -4 y = 2
  9. 9. Answers Y X x-axis y-axis x = 0 y = 0
  10. 10. SLOPE = POSITIVE-UP NEGATIVE-DOWN Slope is a measure of STEEPNESS
  11. 11. The Symbol for SLOPE = m POS. Slope is +m NEG. Slope is -m Think of m for Mountain
  12. 12. SLOPE = • • How much does this line rise? How much does it run? (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 5 6 4
  13. 13. SLOPE = • • How much does this line rise? How much does it run? (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 5 6 4 2 3 3 2
  14. 14. m=SLOPE = • • (3,2) (6,4) (0,0) 1 2 3 1 2 4 3 5 6 4 x 1 y 1 x 2 y 2
  15. 15. Switch points and calculate slope Make (3,2) (x 2 ,y 2 ) & (6,4) (x 1 ,y 1 ) • • (x 2 ,y 2 )(6’4) (x 1 ,y 1 )(3,2) • • (x 1 ,y 1 )(6,4) (x 2 ,y 2 )(3,2)
  16. 16. Recalculation with points switched • • (x 1 ,y 1 )(6,4) (x 2 ,y 2 )(3,2) Same slope as before
  17. 17. It doesn’t matter what 2 points you choose on a line the slope must come out the same
  18. 18. Keeping Track of Signs When Finding The Slope Between 2 Points • Be Neat & Careful • Use (PARENTHASES) • Double Check Your Work as you Go • Follow 3 Steps
  19. 19. 3 Steps for finding the Slope of a line between 2 Points (3,4)&(-2,6) 1st Step: Write x 1 ,y 1 ,x 2 ,y 2 over numbers 2nd Step: Write Formula and Substitute x 1 ,x 2 ,y 1 ,y 2 values. 3rd Step: Calculate & Simplify (3,4) & (-2,6) x 1 y 1 x 2 y 2
  20. 20. Find the Slopes of Lines containing these 2 Points 1. (1,7) & (5,2) 5. (3,6) & (5,-5) 3. (-3,-1) & (-5,-9) 6. (1,-4) & (5,9) 4. (4,-2) & (-5,4) 2. (3,5) & (-2,-8)
  21. 21. 1. (1,7) & (5,2) 5. (3,6) & (5,-5) 3. (-3,-1) & (-5,-9) 6. (1,-4) & (5,9) 4. (4,-2) & (-5,4) 2. (3,5) & (-2,-8) ANSWERS
  22. 22. Solve for y if (9,y) & (-6,3) & m=2/3
  23. 23. Review Finding the Slopes of Lines Given 2 Points 1st Step: Write x 1 ,x 2 ,y 1 ,y 2 over numbers 2nd Step: Write Formula and Substitute x 1 ,x 2 ,y 1 ,y 2 values. 3rd Step: Calculate & Simplify NOTE: Be Neat, Careful, and Precise and Check your work as you go..
  24. 24. ZERO Slope Horizontal Positive Slope Is Up the Hill Negative Slope Is Down the Hill NO Slope Vertical Drop
  25. 25. ZERO Slope Horizontal NO Slope Vertical Drop
  26. 26. Parallel Lines Have the Same Slope • • (0,0) 1 2 3 1 2 4 3 5 6 4 5
  27. 27. Perpendicular Lines Have Neg. Reciprocal Slopes (0,0) 1 2 3 1 2 4 3 5 6

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