Finding Slope 2009

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Finding Slope 2009

  1. 1. Objective  find the slope of a line given a line on a graph. The students will be able to:  find the slope of a line given 2 points on a graph.  find the slope of a line given 1 point and the slope of the graph.
  2. 2. What is the meaning of this sign? <ul><li>Icy Road Ahead </li></ul><ul><li>Steep Road Ahead </li></ul><ul><li>Curvy Road Ahead </li></ul><ul><li>Trucks Entering Highway Ahead </li></ul>
  3. 3. What does the 7% mean? 7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally. So, what is slope??? 7 feet 100 feet Slope is the steepness of a line. 7%
  4. 4. Slope can be expressed differently as: A line has a positive slope if it slopes uphill from left to right . A line has a negative slope if it slopes downhill from left to right .
  5. 5. When given the graph, it is easier to apply “ rise over run ” . Determine the slope of the line given a line on a graph.
  6. 6. Determine the slope of the line. Start with the lower point and count how much you rise and run to get to the other point! 6 3 run 3 6 = = rise Notice the slope is positive! the line slopes upward and to the right 1 2
  7. 7. Find the slope of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula. y 2 is the y coordinate of the 2 nd ordered pair (y 2 = 1) y 1 is the y coordinate of the 1 st ordered pair (y 1 = -2)
  8. 8. Did you notice that both previous examples were the same problem written differently? (-2, -2) and (4, 1) Which method do you think is easiest? You can do the problems either way! 6 3
  9. 9. Find the slope of the line that goes through the points (-1, 2) and (1, 4). a. -1 b. 1 c. 2 d. 4
  10. 10. Determine the slope of the line shown. a. -3 b. 3 c. -3/5 d. 3/5
  11. 11. Determine the slope of the line using any two points on the line. The line is decreasing (slope is negative). 5 -2.5 Choose two points on the graph. Apply rise over run.
  12. 12. What is the slope of a vertical line? <ul><li>Notice the line doesn’t run! </li></ul>All vertical lines have an undefined slope.
  13. 13. What is the slope of a horizontal line? <ul><li>Notice the line doesn’t rise! </li></ul>All horizontal lines have a slope = 0.
  14. 14. Remember the word “VUXHOY” V ertical lines U ndefined slope X = number; this is the equation of the line. H orizontal lines O - zero is the slope Y = number; this is the equation of the line.
  15. 15. Draw a line through the point (2,0) that has a slope of 3. <ul><li>1. Plot the ordered pair (2, 0). </li></ul>1 3 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. <ul><li>Draw a straight line through </li></ul><ul><li>the points. </li></ul>
  16. 16. The slope of a line that goes through points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula continued
  17. 17. We must solve for r (x 1 ), simplify and write as a proportion. x (4 – r ) multiply each side by the common denominator x (4 – r ) 16 – 4 r = -4 continued
  18. 18. Simplify and solve the equation. The ordered pairs are (5, 6) and (4, 2)

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