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Equation of a Straight Line

Equation of a Straight Line. Investigation. y = 2x +1. Fill in table. Write points as coordinates. Draw a coordinates grid and plot points. Draw a line through points. Use your two coordinates to calculate gradient. From your diagram find where the line cuts the Y axis .

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Equation of a Straight Line

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  1. Equation of a Straight Line

  2. Investigation y = 2x +1 Fill in table Write points as coordinates Draw a coordinates grid and plot points Draw a line through points Use your two coordinates to calculate gradient From your diagram find where the line cuts the Y axis (the y intercept!)

  3. Repeat for y = 3x – 2 Fill in table Write points as coordinates Draw a coordinates grid and plot points Draw a line through points Use your two coordinates to calculate gradient From your diagram find where the line cuts the Y axis (the y intercept!) Also y = -2x + 4 y = ½ x – 3

  4. m Y Intercept (0 , 1) y = 2x + 1 2 (0 , -2) y = 3x – 2 3 (0 , 4) y = -2x + 4 -2 (0 , -3) y = ½ x – 3 ½

  5. Equation is related to: • Gradient • Y intercept (cuts Y axis) y (0 ,…) x

  6. 3 (0 , 5) - ½ (0 , 7) EquationGradientY Intercept Y = 3x + 5 Y = - ½ x + 7

  7. 3 (0 , 5) - ½ (0 , 7) EquationGradientY Intercept Y = 3x + 5 Y = - ½ x + 7

  8. 3 (0 , 5) - ½ (0 , 7) EquationGradientY Intercept Y = 3x + 5 Y = - ½ x + 7 Y =8x – 5 Y = -6x + 9 (0, -5) 8 (0, 9) -6

  9. Equation of a Straight Line Is in form y = mx + c Ex 1 y = - ¾ x + 2 m = - ¾ , y int (0 , 2) Ex 2 m = 9, y int (0 , -8) y = 9x - 8 gradient Y intercept (0 ,?)

  10. Write down gradient and Y intercept 1. y = 2x + 4 2. y = ½ x -7 3. y = -5x + 6 4. y = x + 8 5. y = 7x 6. y = 6 + 2x (careful) 7. y = 9 – 3x 8. y = 7

  11. Write down the equation m Y intercept 1. 5 (0 , 7) 2. -5 (0 , 5) 3. ¾ (0 , -6) 4. -5 (0 , -5) 5. 1 (0 , 4) 6. 8 (0 , 0) 7. 0 (0 , 9)

  12. Calculating equation y Gradient? Need 2 points (1 , 2) m = 2 – (-1) 1 - 0 m (x2, y2) c = 3/1 = 3 x (0 , -1) y intercept -1 (x1, y1) Equation y = 3x - 1

  13. Calculating equation y (-2 , 3) Gradient? (x1, y1) Need 2 points (2 , 1) m = 1 – 3 2 – (-2) m (x2, y2) c = -2/4 = - ½ x y intercept 2 Equation y = - ½ x + 2

  14. Special Cases y (0 , 4) (annoying lines!) Horizontal lines Y = 0x + 4 Y = 4 m = 0 x

  15. Special Cases No y intercept! y Vertical lines (really annoying!) (2 , 4) m = ∞ x (2 , 0) (2 , -2)

  16. Special Cases No y intercept! y Vertical lines (really annoying!) (2 , 4) m = ∞ x (2 , 0) (2 , -2) Equation x = 2

  17. Annoying Lines Equations Horizontal Lines (m = 0) are in form y = ? (i.e no x) Vertical lines (m = ∞) are in form x = ? (i.e no y) y Y = 5 (0 , 5) (7 , 0) x X = 7

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