the relationship between x and y is given by the equation 3x-4y = 12 and the range of y is 9, then what is the range of x?

Given the equation \( 3x - 4y = 12 \), we want to find the range of \( x \) when the range of \( y \) is given as \( 9 \).

### Step 1: Express \( x \) in terms of \( y \).
First, solve for \( x \) in the equation:

\[
3x = 4y + 12
\]

\[
x = \frac{4y + 12}{3}
\]

### Step 2: Substitute the given range of \( y \).
If the range of \( y \) is \( 9 \), this implies that \( y \) can take on the value \( 9 \).

### Step 3: Calculate the corresponding value of \( x \).
Substitute \( y = 9 \) into the equation for \( x \):

\[
x = \frac{4(9) + 12}{3} = \frac{36 + 12}{3} = \frac{48}{3} = 16
\]

So, if \( y = 9 \), then \( x = 16 \).

### Conclusion:
If \( y \) is fixed at \( 9 \), then \( x \) will be fixed at \( 16 \). Therefore, the range of \( x \) is simply \( 16 \) when \( y \) is \( 9 \).

Would you like more details on this, or do you have any questions?

### Related Questions:
1. What would be the range of \( x \) if the range of \( y \) were a set of values instead of a single number?
2. How does the slope of the equation \( 3x - 4y = 12 \) affect the relationship between \( x \) and \( y \)?
3. Can you find the intercepts of the line represented by the equation \( 3x - 4y = 12 \)?
4. What is the significance of the constant term in the equation \( 3x - 4y = 12 \)?
5. How would the range of \( x \) change if the equation were modified to \( 3x - 4y = k \) where \( k \) is a constant?

### Tip:
Always isolate one variable to find its dependency on the other when given an equation.

Explore how to determine the range of x when y is fixed in the linear equation 3x - 4y = 12. Learn step-by-step how to solve for x and understand the impact of fixing y on the value of x. Suitable for Grades 7-9 students learning about linear equations and algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation