1 / 43

4.5 Finding The Slope of a Line

4.5 Finding The Slope of a Line. What is the meaning of this sign?. Icy Road Ahead Steep Road Ahead Curvy Road Ahead Trucks Entering Highway Ahead. Slopes are commonly associated with mountains. The slope we are studying is associated with the graph of a line. Definitions of Slope.

evelyn-oneal
Download Presentation

4.5 Finding The Slope of a Line

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.5 Finding The Slope of a Line

  2. What is the meaning of this sign? • Icy Road Ahead • Steep Road Ahead • Curvy Road Ahead • Trucks Entering Highway Ahead

  3. Slopes are commonly associated with mountains.

  4. The slope we are studying is associated with the graph of a line.

  5. Definitions of Slope • The tilt or inclination of a line • The ratio of vertical change to horizontal change. • The change in y over the change in x Δy Δx

  6. Tilt or Inclination FROM LEFT TO RIGHT!!!! SLOPE IS ZERO y = # SLOPE IS UNDEFINED POSITIVE SLOPE NEGATIVE SLOPE x = #

  7. Tell me slope of each line NEGATIVE POSITIVE POSITIVE ZERO

  8. Slope can be expressed different ways: UP or DOWN RIGHT A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right.

  9. Graph (3,2) and (-1,-1)

  10. Draw a line through the points.

  11. Run Rise 4 THE SLOPE IS 3 4 3

  12. Find the slope of the following line. The slope is… 1 2

  13. Find the slope of the line. The slope is…. -3

  14. 1) Determine the slope of the line. When given the graph, it is easier to apply “rise over run”.

  15. Determine the slope of the line shown. • -2 • -½ • ½ • 2

  16. Determine the slope of the line. -2 Find points on the graph. Use two of them and apply rise over run. 1 The line is decreasing (slope is negative).

  17. What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

  18. What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

  19. Find the slope of these lines. • Black line 3 • Red Line 1 • Blue Line -1/2

  20. Find the slope of these lines • Orange line = 0 • Green Line = Undefined

  21. Determining Slope Rise=1 Rise=12 Run =2 Run =4 Rise=6 Run =2 1 2 Slope= Slope=3

  22. Let’s find the slope of a line with two points, WITHOUT LOOKING AT A GRAPH. REMEMBER THE SLOPE FORMULA???!!!!!

  23. Determining Slope without graphing • Find the change in the Y-coordinates by subtracting(rise) • Pick 2 points on the line (2, 5) • Find the change in the X-coordinates by subtracting(run) 5-(-6) = 11 6 (-4, -6) 2-(-4)

  24. 2) 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! y2 is the y coordinate of the 2nd ordered pair (y2 = 1) y1 is the y coordinate of the 1st ordered pair (y1 = -2)

  25. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1). x1 y1 x2 y2

  26. Sample Problems: • Find the slope of the line thru the points given: • (-3,-1) and (-2,4) • (-3,4) and (2,-2) x1 y1 x2 y2 x1 y1 x2 y2

  27. Independent Practice: Calculate the slope for each pair of points. Classify each slope as positive, negative, zero, or undefined. 1. (2, 2) and (3, 5) 2. (0, 0) and (3, 0) Slope: 3 Classification: Positive Slope: 0 Classification: Horizontal 3. (-2, -1) and (-1, -4) 4. (2, 3) and (2, 7) Slope: -3 Classification: Negative Slope: Undefined Classification: Vertical 5. (-1, -1) and (5, 5) 6. (8, 4) and (6, 4) Slope: 1 Classification: Positive Slope: 0 Classification: Zero

  28. EVERYONE GET A COMMUNICATOR!!!

  29. Draw a line through the point (2,0) that has a slope of 3. 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points. 1 3

  30. If you know the slope and one point on the line you can draw the line.Example: slope is 1/3 and the point (-2,-1)

  31. Now you draw a line. • Given: slope is 2/3 and the point is (1,0) • Given: slope is –3 and the point is (–2,4) • Given: slope is 1 and the point is (2,3)

  32. Graph the line y = 3x +1, then tell me the slope of that line after you graphed it. The slope is 3 x y -2 -1 0 1 2 -5 -2 1 4 7

  33. Graph the line 2x + y = 4, then tell me the slope of that line after you graphed it. y = -2x + 4 The slope is -2 x y -2 -1 0 1 2 8 6 4 2 0

  34. Graph the line y = -5, then tell me the slope of that line after you graphed it. The slope is 0 x y -2 -1 0 1 2 -5 -5 -5 -5 -5

  35. Graph the line y = 2x, then tell me the slope of that line after you graphed it. The slope is 2 x y -2 -1 0 1 2 -4 -2 0 2 4

  36. Graph the line y = 3x - 2, then tell me the slope of that line after you graphed it. The slope is 3 x y -2 -1 0 1 2 -8 -5 -2 1 4

  37. Graph the line 2x + 3y = 6, then tell me the slope of that line after you graphed it. The slope is -2/3 x y -6 -3 0 3 6 6 4 2 0 -2

  38. Graph the line y = -x - 2, then tell me the slope of that line after you graphed it. The slope is -1 x y -2 -1 0 1 2 0 -1 -2 -3 -4

  39. Graph the line 3x – 4y = 12, then tell me the slope of that line after you graphed it. The slope is 3/4 x y -8 -4 0 4 8 -9 -6 -3 0 3

  40. Graph the line x – y = 5, then tell me the slope of that line after you graphed it. y = x - 5 The slope is 1 x y -2 -1 0 1 2 -7 -6 -5 -4 -3

  41. The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula

  42. To solve for r, simplify and write as a proportion. Cross multiply. 4(4 – r) 1(-4) =

  43. Simplify and solve the equation.1(-4) = 4(4 – r) -4 = 16 – 4r -16 -16 -20 = -4r -4 -4 5 = r The ordered pairs are (5, 6) and (4, 2)

More Related