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Math Asked by a SnapAndSolve user · about 9 hours ago

Calculate the slope of each linear relationship using the formula. Show all your work. a. Number of...

1. Calculate the slope of each linear relationship using the formula. Show all your work.
a. Number of Carnival Ride Tickets | Cost (dollars)
4 | 9
8 | 12
16 | 18
32 | 30
b. -1 | -13
0 | -2
2 | 8
5 | 25
2. Analyze the values in the table before you start calculating the rate of change. Do you think the rate of change is positive or negative?
3. Days Passed | Vitamins Remaining in Bottle
0 | 25
1 | 23
2 | 21
3 | 19
4. 1 | 7
2 | 10
3 | 16
4 | 29
5 | 40

Answer

  1. a. To calculate the slope, use the formula: slope = (y2 - y1) / (x2 - x1).
    For the first two points (4, 9) and (8, 12):
    Slope = (12 - 9) / (8 - 4) = 3 / 4 = 0.75.
    For the next two points (8, 12) and (16, 18):
    Slope = (18 - 12) / (16 - 8) = 6 / 8 = 0.75.
    For the last two points (16, 18) and (32, 30):
    Slope = (30 - 18) / (32 - 16) = 12 / 16 = 0.75.
    The slope is consistent at 0.75.

    b. For the first two points (-1, -13) and (0, -2):
    Slope = (-2 + 13) / (0 + 1) = 11 / 1 = 11.
    For the next two points (0, -2) and (2, 8):
    Slope = (8 + 2) / (2 - 0) = 10 / 2 = 5.
    For the last two points (2, 8) and (5, 25):
    Slope = (25 - 8) / (5 - 2) = 17 / 3 ≈ 5.67.
    The slope varies, indicating a non-linear relationship.

  2. The rate of change is positive if the values increase as you move from left to right in the table, and negative if they decrease. Analyze each table to determine this before calculating.

  3. To calculate the slope for the vitamins remaining:
    For the first two points (0, 25) and (1, 23):
    Slope = (23 - 25) / (1 - 0) = -2 / 1 = -2.
    For the next two points (1, 23) and (2, 21):
    Slope = (21 - 23) / (2 - 1) = -2 / 1 = -2.
    For the last two points (2, 21) and (3, 19):
    Slope = (19 - 21) / (3 - 2) = -2 / 1 = -2.
    The slope is consistent at -2, indicating a negative rate of change.

  4. To calculate the slope for the last set of values:
    For the first two points (1, 7) and (2, 10):
    Slope = (10 - 7) / (2 - 1) = 3 / 1 = 3.
    For the next two points (2, 10) and (3, 16):
    Slope = (16 - 10) / (3 - 2) = 6 / 1 = 6.
    For the last two points (3, 16) and (4, 29):
    Slope = (29 - 16) / (4 - 3) = 13 / 1 = 13.
    The slope varies, indicating a non-linear relationship.

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