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Writing Equations

Writing Equations. Index Card Activity. I. How to Write an Equation of a Line Given m and b. 1. Write down y = m x + b 2. Substitute slope for m and y-intercept for b . 3. Simplify the equation. Write the equation of the line given m and b.

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Writing Equations

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  1. Writing Equations Index Card Activity

  2. I. How to Write an Equation of a LineGiven m and b 1. Write down y = mx + b 2. Substituteslope for m and y-intercept for b. 3. Simplify the equation

  3. Write the equation of the line given m and b. Ex. 1 Slope is -5 and y-intercept is 2 y = -5x + 2 Ex. 2 Slope is -1/2 and y-intercept is -2 y = -½x – 2

  4. II. How to Write an Equation of a Line Given a Graph Write down y = mx + b Use any 2 “good” points on the graph to find the slope, m. Find the y-intercept on the graph, b. Substituteslope for m and y-int for b into the equation y = mx + b.

  5. 5. Write the equation of this graph  m = = y = mx + b y = x + b y = x + 2 

  6. 7. Write the equation of this graph M = = = -3 y = mx + b y = -3x + b   y = -3x + 2

  7. III. How to Write an Equation of a Line Given m and a point Write down y = mx + b. Substitute slope for m and the point (x, y). Solve for b. Substitute m and b back into the equation.

  8. Write the equation of the line given m and a point Ex 13: m = 2 Point: (2, 3) y = mx + b 3 = 2 (2) + b 3 = 4 + b (subtract 4 from both sides) -1 = b y = 2x – 1

  9. Write the equation of the line given m and a point Ex 15: m = -2 Point: (-5, 3) y = mx + b 3 = -2 (-5) + b 3 = 10 + b (subtract 10 from both sides) -7 = b y = -2x – 7

  10. IV. How to Write an Equation of a Line Given TWO points Write down y = mx + b. Use the slope formula to find m. Pick one of the ordered pairs & substitute slope for m and the point (x, y). Solve for b. Substitute m and b into the equation.

  11. Equation of a Line - Given 2 points Ex: 21 (2, 3) (4, 5) y = mx + b 3 = 1(2) + b 3 = 2 + b (subtract 2 both sides) b = 1 y = x + 1

  12. Equation of a Line - Given 2 points Ex: 23 (2, 2) (0, 4) y = mx + b y = -1x + b 4 = -1 (0) + b 4 = 0 + b 4 = b y = -x + 4

  13. How to Write an Equation of a LinePARALLEL to another and given a point • 1. Given equation should be solved for y (y = mx + b) • Write down the slope of that line • Substitute m and (x, y) in y = mx + b. • Solve for b. • Write the equation using m and b.

  14. Write a line parallel to the line y = 3x – 5 and passes through the point (-5, -2). y = mx + b y = 3x + b -2 = 3 (-5) + b -2 = -15 + b (add 15 to each side) 13 = b y = 3x + 13

  15. Write a line parallel to the line 2x + y = 3 and passes through the point (-2, 5). Rewrite equation: y = -2x + 3 y = mx + b Y = -2x + b 5 = -2 (-2) + b 5 = 4 + b (subtract 4 from each side) 1 = b y = -2x + 1

  16. How to Write an Equation of a LinePERPENDICULAR to another and given a point • 1. Given equation should be solved for y (y = mx + b) • Write down the OPPOSITE RECIPROCAL slope of that line • Substitute m and (x, y) in y = mx +b. • Solve for b. • Write the equation using m and b.

  17. Write a line perpendicular to the line y = ½ x – 2 and passes through the point (1, 0). Find opposite reciprocal of ½: -2 y = mx + b y = -2x + b 0 = -2 (1) + b 0 = -2 + b (add 2 to each side) 2 = b y = -2x + 2

  18. Write a line perpendicular to the line 2x + 3y = 9 and passes through the point (6, -1). Rewrite equation: 3y = -2x + 9 (divide both sides by 3) y = x + 3 Find opposite reciprocal of : y = mx + b y = x + b -1 = (6) + b -1 = + b -1 = 9 + b (subtract 9 from both sides) -10 = b y = 3/2 x – 10

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