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6.6 Warm-up

6.6 Warm-up. Objective 3. The graph of which function is shown ? a. Y = 30x b. Y = 30 - x c. Y = 30 - (x+5) d. y = 30 - 5x. y. 30. 20. 10. x. 0. 0 2 4 6. Pardekooper. 6.6 Warm-up. Objective 3. The graph of which function is shown ? a. Y = 30x

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6.6 Warm-up

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  1. 6.6 Warm-up Objective 3 The graph of which function is shown ? a. Y = 30x b. Y = 30 - x c. Y = 30 - (x+5) d. y = 30 - 5x y 30 20 10 x 0 0 2 4 6 Pardekooper

  2. 6.6 Warm-up Objective 3 The graph of which function is shown ? a. Y = 30x b. Y = 30 - x c. Y = 30 - (x+5) d. y = 30 - 5x y 30 20 10 x 0 0 2 4 6 Pardekooper

  3. Parallel & Perpendicular Lines Pardekooper

  4. What you’ll learn To determine if two lines are parallel or perpendicular by their slopes, and To write equations of lines that pass through a given point, parallel or perpendicular to the graph of the given equation Pardekooper

  5. Here are some terms. Two lines are parallel if and only if they have the same slope. example: Two lines are perpendicular if and only if their slopes are opposite inverses. example: Pardekooper

  6. Is the following set of lines parallel or perpendicular? Lets try some. y=2x+3 y=2x-5 parallel Pardekooper

  7. Is the following set of lines parallel or perpendicular? Lets try some. y=1/2x+3 y= -2x-5 perpendicular Pardekooper

  8. Is the following set of lines parallel or perpendicular? Lets try some. y=1/4x+1 y=4x-1 neither Pardekooper

  9. Write the equation for the that is parallel to y=5x-1 with y-intercept of 2. Where do the equations come from? m=5 b=2 y=mx+b y=5x+2 Pardekooper

  10. Write the equation for the that is parallel to y=2/3x-1 with y-intercept of -1. Where do the equations come from? m=2/3 b=-1 y=mx+b y=2/3x-1 Pardekooper

  11. Write the equation for the that is perpendicular to y=2/3x-1 with y-intercept of -4. Where do the equations come from? m=-3/2 b=-4 y=mx+b y=-3/2x-4 Pardekooper

  12. Write the equation for the that is perpendicular to y=-1/4x-1 with y-intercept of 5. Where do the equations come from? m=4/1 b=5 y=mx+b y=4x+5 Pardekooper

  13. Write an equation for a line that passes through the point (1,3)and is parallel to y=2x+4. Where do the equations come from? m=2 P(1,3) y-y1=m(x-x1) y-3=2(x-1) Pardekooper

  14. Write an equation for a line that passes through the point (2,-4)and is parallel to y=2/3x+4. Where do the equations come from? m=2/3 P(2,-4) y-y1=m(x-x1) y-(-4)=2/3(x-2) Pardekooper

  15. Write an equation for a line that passes through the point (1,-3)and is perpendicular to y=2/3x+1. Where do the equations come from? m=-3/2 P(1,-3) y-y1=m(x-x1) y-(-3)=-3/2(x-1) Pardekooper

  16. Why do we need to know if lines are parallel or perpendicular ? Given a pair of opposite sides of a quadrilateral are parallel, what does the quadrilateral look like ? Pardekooper

  17. Why do we need to know if lines are parallel or perpendicular ? Given a pair of opposite sides of a quadrilateral are parallel and equal in length,what does the quadrilateral look like ? Given a pair of opposite sides of a quadrilateral are parallel, what does the quadrilateral look like ? In order to know which one, you need more information. Pardekooper

  18. Why do we need to know if lines are parallel or perpendicular ? Given a pair of opposite sides of a quadrilateral are parallel and equal in length, and a pair of adjacent sides form a right angle,what does the quadrilateral look like ? Given a pair of opposite sides of a quadrilateral are parallel and equal in length,what does the quadrilateral look like ? We need some more information. Pardekooper

  19. 3.7 Slopes of Parallel and Perpendicular Lines Geometry Are the lines parallel, perpendicular or neither 1. y = -5x 2. y=3x+1 3. y=1/2x-4 y = 5x - 18 y=-1/3x+4 y=1/2x+4 Write an equation for a line that passes through the point and is parallel to the given equation. 4. (2,-7), y = x - 2 5. (1,-2), y = -2x + 7 6. (2,-1), y = -0.5x + 2 Write an equation for a line that passes through the point and is perpendicular to the given equation. 7. (6,-2), y = 3/5x - 4 8. (3,7), y = 3/4x -1 9. Write an equation of the line that has an y-intercept of 3 and is perpendicular to the graph of 5x - 3y = 2. 10. Use slope to show that opposite sides of hexagon RSTUVW are parallel. 11. Use slope to determine whether a triangle with vertices G(3,2), H(8,5), and K(0,10) is a right triangle. R S T W V U

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