What is the constant of proportionality?
Understand the Problem
The question provides a table of x and y values that have a proportional relationship, and asks you to find the constant of proportionality.
Answer
$\frac{3}{4}$
Answer for screen readers
The constant of proportionality is $\frac{3}{4}$.
Steps to Solve
- Understanding Proportional Relationships
A proportional relationship between two variables, $x$ and $y$, can be expressed as $y = kx$, where $k$ is the constant of proportionality. This means that the ratio $\frac{y}{x}$ is always equal to $k$.
- Calculate the constant of proportionality
To find $k$, we can use any pair of $x$ and $y$ values from the table. Let's use the first pair: $x = 8$ and $y = 6$.
- Finding k
Substitute these values into the equation $y = kx$ and solve for $k$:
$6 = k \cdot 8$
Divide both sides by 8:
$ k = \frac{6}{8} $
- Simplify the fraction
Simplify the fraction $\frac{6}{8}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$k = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$
The constant of proportionality is $\frac{3}{4}$.
More Information
The constant of proportionality is also known as the unit rate, because it tells you how much $y$ changes for every one unit change in $x$.
Tips
A common mistake is to confuse the ratio and calculate $k = \frac{x}{y}$ instead of $k = \frac{y}{x}$. This would lead to finding the reciprocal of the correct constant of proportionality.
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