The value of y is directly proportional to the value of x. When x = 3, y = 10. What is the value of y when x = 9?
Understand the Problem
The question asks to find the value of y when x is equal to 9, given that y is directly proportional to x with a specific point of reference (when x = 3, y = 10). This indicates that we should first determine the constant of proportionality and then use it to find the new value of y.
Answer
The value of $y$ when $x = 9$ is $30$.
Answer for screen readers
The value of $y$ when $x = 9$ is $30$.
Steps to Solve
-
Identify the relationship Since $y$ is directly proportional to $x$, we can express this relationship with the equation: $$ y = kx $$ where $k$ is the constant of proportionality.
-
Find the constant of proportionality Using the provided information ($x = 3$ and $y = 10$), we can substitute these values into the equation to find $k$: $$ 10 = k \cdot 3 $$ To find $k$, divide both sides by 3: $$ k = \frac{10}{3} $$
-
Set up the equation with the constant Now that we have $k$, we can express $y$ in terms of $x$: $$ y = \frac{10}{3}x $$
-
Calculate the value of y when x = 9 Substituting $x = 9$ into the equation gives us: $$ y = \frac{10}{3} \cdot 9 $$ To simplify: $$ y = \frac{90}{3} = 30 $$
The value of $y$ when $x = 9$ is $30$.
More Information
This example illustrates direct proportionality, where the relationship between two variables remains constant. In this case, when $x$ is tripled (from 3 to 9), $y$ also triples (from 10 to 30).
Tips
- Forgetting to find the constant of proportionality first: It's crucial to calculate $k$ before finding $y$ for a different $x$.
- Incorrect substitution: Ensure the correct values are substituted back into the equation.
