Find the constant of variation
Key Notes :
Constant of Variation
- In a proportional relationship, the constant of variation is the constant ratio between the two quantities.
- It represents the rate at which one quantity changes with respect to the other.
Finding the Constant of Variation
- Identify the proportional relationship: Determine if the relationship between the two quantities is proportional.
- Find a pair of corresponding values: Choose any pair of corresponding values for the two quantities.
- Calculate the ratio: Divide the value of the second quantity by the value of the first quantity.
- The result is the constant of variation.
Example:
Consider the following table of values:
| x | y |
|---|---|
| 2 | 6 |
| 4 | 12 |
| 6 | 18 |
| 8 | 24 |
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To find the constant of variation, calculate the ratio of y to x for any pair of values:
- 6/2 = 3
- 12/4 = 3
- 18/6 = 3
- 24/8 = 3
Therefore, the constant of variation is 3.
Key Points to Remember:
- The constant of variation is the constant ratio between two quantities in a proportional relationshi
Learn with an example
This graph shows how the total number of pieces Lola has learnt depends on the number of weeks she has taken piano lessons.
What is the constant of variation?
Write your answer as a decimal or integer.
_______pieces per week.
Find any two points on the line.
Two points on the line are (0, 0) and (2, 3). Put those points into the slope formula.
slope = change in y/change in x
= 3-0/2-0 Plug in (0, 0) and (2, 3)
= 3/2 Subtract
= 1.5 Write as a decimal
The slope is 1.5. The constant of variation is 1.50 pieces per week.
This graph shows how the total number of souvenirs Vijay buys is related to the number of days he spends on holiday.
What is the constant of variation?
Write your answer as a decimal or integer.
_______souvenirs per day.
Find any two points on the line.
Two points on the line are (0, 0) and (40, 30). Put those points into the slope formula.
slope = change in x/change in y
=30-0/40-0 Plug in (0, 0) and (40, 30)
= 30/40 Subtract
=3/4 Simplify
= 0.75 Write as a decimal
The slope is 0.75. The constant of variation is 0.75 souvenirs per day.
This graph shows how the length of Frank’s essay depends on the number of hours he spends writing this week.
What is the constant of variation?
Write your answer as a decimal or integer.
______pages per hour.
Find any two points on the line.
Two points on the line are (0, 0) and (40, 10). Put those points into the slope formula.
slope = change in y/change in x
= 10-0/40-0 Plug in (0, 0) and (40, 10)
= 10/40 Subtract
= 1/4 Simplify
= 0.25 Write as a decimal
The slope is 0.25. The constant of variation is 0.25 pages per hour.
let’s practice!
