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4.4 The Slope-Intercept Form of the Equation of a Line

4.4 The Slope-Intercept Form of the Equation of a Line. Slope-Intercept Form. The slope-int. form of an eqn. of a line with slope m and y-intercept b is y = m x + b slope y-int Ex. Find the eqn. of a line with slope 4 and y-int 1. y = m x + b m = 4 , b = 1

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4.4 The Slope-Intercept Form of the Equation of a Line

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  1. 4.4 The Slope-Intercept Form of the Equation of a Line

  2. Slope-Intercept Form The slope-int. form of an eqn. of a line with slope m and y-intercept b is y = mx + b slope y-int Ex. Find the eqn. of a line with slope 4 and y-int 1. y = mx + b m = 4, b = 1 y = 4x + 1

  3. Ex. Find the slope and y-intercept of y = ¼x – 2. y = ¼x – 2 y = ¼x + (-2) m = ¼, b = -2 or (0, -2) Ex. Find the slope and y-intercept of y = -5x. y = -5x + 0 m = -5, b = 0 or (0, 0)

  4. Ex. Find the slope and y-intercept of 4x – 2y = 8. We need to solve for y first (put in slope-int. form y=mx + b) 4x – 2y = 8 4x – 2y – 4x = 8 – 4x -2y = -4x + 8 -2y = -4x + 8 -2 -2 -2 y = 2x – 4 m = 2,b = -4

  5. Graphing Using Slope and Y-Intercept y = mx + b slope y-int: b or (0, b) • Solve the eqn. for y (put in slope-int form) • Plot the y-int. b or (0, b) • Use slope to plot next point • Draw line

  6. Ex. Graph y = 2x – 1 using slope and y –intercept. y • y = 2x – 1 m = 2, b = -1 or (0, -1) • Plot (0, -1) • Using rise = 2 and run = 1, go up 2 units and right 1 unit to end up at (1, 1) for a 2nd point. • Draw line 3 2 run= 1 1 rise = 2 x 3 -3 -2 -1 1 2 -1 -2 -3

  7. Ex. Graph y = -½x using slope and y –intercept. y • y = -½ x + 0 m = -½, b = 0 or (0, 0) • Plot (0, 0) • Using rise = -1 and run = 2, go down 1 unit and right 2 units to end up at (2, -1) for a 2nd point. • Draw line 3 2 1 x 3 -3 -2 -1 1 2 rise = -1 -1 run = 2 -2 -3

  8. Ex. Graph 5x – 3y = 9 using slope and y –intercept. y • Solve for y: 5x – 3y = 9 5x – 3y – 5x = 9 – 5x -3y = -5x + 9 -3y = -5x + 9 -3 -3 -3 y = 5/3 x – 3 m = 5/3, b = -3 or (0, -3) • Plot (0, -3) • Using rise = 5 and run = 3, go up 5 units and right 3 units to end up at (3, 2) for a 2nd point. • Draw line 3 run = 3 2 1 rise = 5 x 3 -3 -2 -1 1 2 -1 -2 -3

  9. Ex. Graph the following lines. Are the lines parallel, perpendicular, or neither? Explain why. y y = 3x + 1 y = 3x – 3 1) y = 3x + 1 m = 3, b = 1 • y = 3x – 3 m = 3, b = -3 The lines are parallel because they have the same slope, but different y-intercepts. 3 2 1 x 3 -3 -2 -1 1 2 -1 -2 -3

  10. Ex. Write an eqn. in slope-int form (y=mx+b) of the line described: The y-intercept is -7 and the line is perpendicular to the line -¼x + y = 5. • Find slope by putting -¼x + y = 5 in slope-int. form. -¼x + y = 5 -¼x + y + ¼x = 5 + ¼x y = ¼x + 5 Since m = ¼, the slope of the perp. line is m=-4 (neg. recip.) • Now, b = -7 (given to us) and m = -4 (from step 1) so our line is: y = mx + b y = -4x – 7

  11. Groups Page 263: 61, 65, 67, 71

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