Constant of Proportionality Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
easyA car travels 60 miles per hour. Write the equation relating distance \(d\) and time \(t\). What is the constant of proportionality?
Solution
- 1 The relationship is \(d = k \cdot t\) where \(k\) is the constant of proportionality.
- 2 Here, speed = 60 mph, so \(k = 60\).
- 3 Equation: \(d = 60t\).
- 4 In 3 hours: \(d = 60 \times 3 = 180\) miles.
Answer
\(d = 60t\); \(k = 60\)
In \(y = kx\), \(k\) is the constant of proportionality — the unit rate. Here \(k = 60\) miles per hour.
About Constant of Proportionality
The constant ratio between two proportional quantities: if , then is the constant of proportionality.
Learn more about Constant of Proportionality →More Constant of Proportionality Examples
Example 2 medium
The table shows (x) and (y): (2, 10), (4, 20), (6, 30). Is this proportional? Find (k).
Example 3 easyApples cost $0.75 each. Write the equation for cost (C) given quantity (q). Find the cost of 8 apple
Example 4 mediumIf (y = kx) and (y = 35) when (x = 7), find (k) and predict (y) when (x = 12).