Initial Publication Date: August 20, 2014
Calculating Slope: Practice Problems
You can download the questions if you would like to work them on a separate sheet of paper.
Problem 1:
What is the slope of this line in the following graph, and what does it tell us about the relationship between consumption and income?
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Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
Because it is a straight line the slope can be found by calculating the rise/run between any two points. One solution is worked out below:
- Change in income between $0 and $10,000 is $10,000. This is the run.
- Change in consumption between $5,000 and $13,000 is $8,000. This is the rise.
- Rise/Run = 8,000/10,000 = 0.8
The slope is 0.8.
This shows that 0.8 (or 80%) of every increase in income is spent as consumption.
Problem 2:
When Nintendo cut its Playstation price in Japan from $250 to $150, sales increased from 5,000 to 25,000 units as shown in the graph below. What was the increase in sales per one dollar reduction in price for the Playstation?
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- run (∆X) = change in sales = 25,000 - 5,000 = 20,000
- rise (∆Y) = change in price = $250 - $150 = $100
- slope = rise/run = ∆Y/∆X = -$100 / 20,000 = -$1 / 200.
For every one-dollar reduction in price, 200 more Playstations were sold.
Problem 3:
When irrigated water is added to California cotton farms, production revenue increases as shown in the graph. At 8 gallons per plant, what is the increased cotton production revenue for one more gallon of water per plant?
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- run (∆X) = 8 - 0 = 8 gallons
- rise (∆Y) = $19 million - $16 million = $3 million
- slope = rise/run = ∆Y/∆X = $3 million/8 gallons =
0.375 million dollars per gallon per plant
Problem 4:
A car dealership finds that sales increase when interest rates fall as shown in the graph. When interest rates go down by 1% how much do car sales increase by?
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- run (∆X) = 40 - 20 = 20
- rise (∆Y) = 6% - 7% = -1%
- slope = rise/run = ∆Y/∆X = -1/20 =
20 more cars sell when the interest rate falls by 1%
Problem 5:
An oil-producing nation pumps oil from its reserves based on current world oil prices. How much more oil is pumped for a $1 increase in oil prices when the oil price is $100 per barrel?
Provenance: Jeffrey Sarbaum, University of North Carolina at Greensboro
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
- run (∆X) = 90 - 40 = 50 million barrels
- rise (∆Y) = 100 - 0 = $100
- slope = rise/run = ∆Y/∆X = 100/50 = $1 / 0.5 million barrels =
0.5 million more barrels pumped per one dollar increase
Problem 6:
Use the information in the following table to calculate the slope of the supply curve for an ebook sold by Amazon.
| Price |
$10 |
$15 |
| Number of books sold (in thousands) |
17.4 |
10 |
- run (∆X) = 10 - 17.4 = -7.4 thousand books
- rise (∆Y) = $15 - $10 = $5
- slope = rise/run = ∆Y/∆X = 5 / -7.4 = -0.68
Problem 7:
The figure shows a time series graph of the size of the US male and female labor force from 1950 through 2010.
Provenance: Peter Schuhmann, University of North Carolina-Wilmington
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
The slope of labor force participation for women is:
- greater in most years than the slope of the labor force participation for men
- less in most years than the slope of the labor force participation for men
- about the same as the the slope of the labor force participation for men
A: The slope is steeper in most years for women, indicating a larger change in the size of female labor force.
Problem 8:
Provenance: Peter Schuhmann, University of North Carolina-Wilmington
Reuse: This item is offered under a Creative Commons Attribution-NonCommercial-ShareAlike license http://creativecommons.org/licenses/by-nc-sa/3.0/ You may reuse this item for non-commercial purposes as long as you provide attribution and offer any derivative works under a similar license.
According to the figure, over time the slope of labor participation:
- increases for men; falls for women
- decreases for men; increases for women
- increases for men; increases for women
- decreases for men; decreases for women
D: The slope decreases for both men and women, showing a slowing in the growth of the labor force for both.
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