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Warm-up

This lesson focuses on finding slopes of parallel and perpendicular lines, as well as identifying the relationship between the slopes. Practice problems and interactive activities are included.

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Warm-up

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  1. Warm-up 1) Find the measure of angles a, b and c. 2) Find the slope between the points (-2, 8) and (14, 40)

  2. Slope

  3. Let’s look at the slopes of PARALLEL LINES • Use each side of your ruler to draw two parallel lines on your graph paper. • Find 2 points on each line (pick nice ones that lie on the cross of grid lines) • Figure out each path you’d have to walk if the boxes were city blocks between each pair of points. • Count the boxes you moved up or down, then count the boxes you moved left or right • Write it as a fraction • How do the slopes of each line compare?

  4. Let’s look at the slopes of PERPENDICULAR LINES • Draw a line. Place your protractor on that line, and mark a point at the 90° point & where the vertex of the angle should be. • Draw a line through those two points. These lines are now perpendicular. • Find 2 points on each line (pick nice ones that lie on the cross of grid lines). • Figure out the path you’d have to walk if the boxes were city blocks on each line. • Count the boxes you moved up or down, then count the boxes you moved left or right • Write it as a fraction. • How do the slopes of each line compare?

  5. Slope - The ratio of the vertical change to the horizontal change between two points on a line. (Rise over Run) Formula: m =

  6. Practice Finding Slope • Find the slope of the line through (3, 2) and (-1, 6) • Find the slope of the line through (5, -1) and (2, -7) • Find the slope of the line through (2, -3) and (2, 8)

  7. Positive v. Negative Slope

  8. Horizontal Lines m =

  9. Vertical Lines m =

  10. Slopes of Parallel and Perpendicular Lines Parallel Lines – Slopes are the same Perpendicular Lines – Slopes are opposite reciprocals

  11. Does order matter? Find the slope of the line passing through (7, 3) and (5, 9). Here is how they solved the problem: Jose Jeffrey Mike Maria

  12. Does order matter? (7, 3) represents ( x1 , y1)(5, 9) represents ( x2 , y2) (7, 3) represents ( x2 , y2)(5, 9) represents ( x1 , y1) Jose Jeffrey Mike Maria (7, 3) represents ( x2 , y1)(5, 9) represents ( x1 , y2) (7, 3) represents ( x1 , y2)(5, 9) represents ( x2 , y1)

  13. 4) Find the slope of a line parallel to the line that passes through (2, 3) and (4, 7) • Find the slope of a line perpendicular to the line that passes through (-1, 0) and (4, 7) • Find the slope of the line through the points (7, 0) and (7, -3).

  14. 3 Point Quiz • Graph and find the slope of a line through the points A(-7, 5) and B(7, -5) • What is the slope of a line that is perpendicular to line AB?

  15. Homework • p. 136, 1-6, 10

  16. Flipped

  17. Pop Quiz Find the slope of the lines through the following two points: (2pts) (2, 8) and (-3, 15)

  18. Let’s look at the slopes of PARALLEL LINES • Use each side of your ruler to draw two parallel lines on your graph paper. • Find 2 points on each line (pick nice ones that lie on the cross of grid lines) • Figure out each path you’d have to walk if the boxes were city blocks between each pair of points. • Count the boxes you moved up or down, then count the boxes you moved left or right • Write it as a fraction • How do the slopes of each line compare?

  19. Let’s look at the slopes of PERPENDICULAR LINES • Draw a line. Place your protractor on that line, and mark a point at the 90° point & where the vertex of the angle should be. • Draw a line through those two points. These lines are now perpendicular. • Find 2 points on each line (pick nice ones that lie on the cross of grid lines). • Figure out the path you’d have to walk if the boxes were city blocks on each line. • Count the boxes you moved up or down, then count the boxes you moved left or right • Write it as a fraction. • How do the slopes of each line compare?

  20. Slope - The ratio of the vertical change to the horizontal change between two points on a line. (Rise over Run) Formula: m =

  21. Practice Finding Slope • Find the slope of the line through (3, 2) and (-1, 6) • Find the slope of the line through (5, -1) and (2, -7) • Find the slope of the line through (2, -3) and (2, 8)

  22. ROUNDTABLE!

  23. Rules • Do what the slide says on your whiteboard. When a slide changes, rotate your whiteboard with your group. Do not erase your whiteboard unless the slide says to.

  24. Erase your whiteboard and pick two new points.

  25. Find the change in y.

  26. Find the change in x.

  27. Find the slope.

  28. Find the slope of a parallel line.

  29. Find the slope of a perpendicular line.

  30. Graph a line through your given points.

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