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Questions and Answers
What is the slope of the line that passes through the points (0, -2) and (3, 4)?
What is the slope of the line that passes through the points (0, -2) and (3, 4)?
- -2
- 2 (correct)
- 1.5
- 3
If the cost of candy is $3 for every ounce, what is the rate of change represented by the slope?
If the cost of candy is $3 for every ounce, what is the rate of change represented by the slope?
- $2 for every ounce
- $0.50 for every ounce
- $3 for every ounce (correct)
- $1.00 for every ounce
Using the points (-4, -4) and (8, 4), what is the calculated slope of the line?
Using the points (-4, -4) and (8, 4), what is the calculated slope of the line?
- 3/4
- 2/3 (correct)
- 1/2
- 5/6
If the slope indicates that a candle burns down at a rate of 2/3 inches for every 12 minutes, how many inches does it burn down in 10 minutes?
If the slope indicates that a candle burns down at a rate of 2/3 inches for every 12 minutes, how many inches does it burn down in 10 minutes?
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What is the overall implication when a slope of 3 is derived from a graph that depicts cost per ounce of candy?
What is the overall implication when a slope of 3 is derived from a graph that depicts cost per ounce of candy?
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Study Notes
Slope Calculation for Lines
- Slope represents the rate of change in a line graph, calculated using the formula m = (y2 - y1) / (x2 - x1).
- For a line through points (0, -2) and (3, 4):
- y2 = 4 and y1 = -2
- x2 = 3 and x1 = 0
- Calculation yields a slope of m = (4 - (-2)) / (3 - 0) = 6 / 3 = 2.
Cost of Candy as a Function
- The graph illustrates the cost of candy per ounce, with several potential rates:
- 3,3, 3,0.38, 2.66,and2.66, and 2.66,and0.50 per ounce.
- Slope provides insight into the price increase relative to weight.
Candle Burning Rate
- The graph tracks candle height (y) against time in minutes (x).
- Selected points (-4, -4) and (8, 4):
- y2 = 4 and y1 = -4
- x2 = 8 and x1 = -4
- Slope calculation: m = (4 - (-4)) / (8 - (-4)) results in m = 8 / 12 = 2 / 3.
- Equivalent to a burning rate of 1 inch every 10 minutes, indicating the time taken for height reduction.
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