Question

In the \( xy \)-plane, the equation of line \( k \) is \( 3x - 2y = 0 \). Compare:
Quantity A: The \( x \)-intercept of line \( k \)
Quantity B: The \( y \)-intercept of line \( k \)

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.
• E.

Hint:

Always find intercepts by substituting the other variable as zero. This works directly for any line equation.

Answer 1

The Correct Option is C

Step 1: Find the \( x \)-intercept.
To find the \( x \)-intercept, set \( y = 0 \) in the equation: \[ 3x - 2(0) = 0 \quad \Rightarrow \quad 3x = 0 \quad \Rightarrow \quad x = 0. \] So, the \( x \)-intercept is 0.
Step 2: Find the \( y \)-intercept.
To find the \( y \)-intercept, set \( x = 0 \): \[ 3(0) - 2y = 0 \quad \Rightarrow \quad -2y = 0 \quad \Rightarrow \quad y = 0. \] So, the \( y \)-intercept is also 0.
Step 3: Compare.
Both the \( x \)-intercept and \( y \)-intercept are equal to 0.
Step 4: Conclusion.
Thus, \[ \boxed{\text{(C) The two quantities are equal.}} \]