Finding the Constant of Proportionality
Finding the constant of proportionality is a Grade 7 math skill from Yoshiwara Intermediate Algebra where students identify the constant k in a proportional relationship y = kx. By dividing y by x for any data point, students determine k and write the complete proportional equation.
Key Concepts
Property If you know that two variables vary inversely and have one corresponding pair of values, you can find the constant of variation, $k$. Given a point $(x 1, y 1)$, you can calculate $k = x 1 y 1$ and write the specific formula $y = \frac{k}{x}$.
Examples The current, $I$, in a circuit varies inversely with resistance, $R$. An iron with 12 ohms of resistance draws 10 amps. First, find $k = I \cdot R = 10 \cdot 12 = 120$. The formula is $I = \frac{120}{R}$.
Using the formula $I = \frac{120}{R}$, how much current is drawn by a device with 20 ohms of resistance? Substitute $R=20$ to get $I = \frac{120}{20} = 6$ amps.
Common Questions
What is the constant of proportionality?
The constant of proportionality k is the ratio y/x in a direct variation y = kx. It is constant for all pairs in a proportional relationship.
How do you find k from a table of values?
Divide y by x for any row in the table. If the ratio is always the same, the relationship is proportional and k is that ratio.
What does k represent in y = kx?
k is the unit rate — it tells you how much y changes for each one-unit increase in x.
How is finding k related to slope?
In a direct variation y = kx, the constant k is the slope of the line. The line passes through the origin with slope k.