Question

The equation of a line in the intercept form is:

• A. \( \frac{x}{a} + \frac{y}{b} = 1 \)
• B. \( \frac{x}{a} + \frac{y}{b} = ab \)
• C. \( ax + by = c \)
• D. None of these

Hint:

The intercept form of a line is useful for quickly identifying the x- and y-intercepts of a line.

Answer 1

The Correct Option is A

Step 1: Understanding the intercept form of the equation of a line.
The intercept form of the equation of a line is given by: \[ \frac{x}{a} + \frac{y}{b} = 1 \] where \( a \) and \( b \) are the x- and y-intercepts, respectively.
Step 2: Explanation of options.

• (A) \( \frac{x}{a} + \frac{y}{b} = 1 \): Correct. This is the correct form of the intercept form of the equation of a line.
• (B) \( \frac{x}{a} + \frac{y}{b} = ab \): Incorrect. This is not the correct form of the intercept equation.
• (C) \( ax + by = c \): Incorrect. This is the general form of a linear equation, not the intercept form.
• (D) None of these: Incorrect. Option (A) is correct.

Step 3: Conclusion.
The correct answer is (A) \( \frac{x}{a} + \frac{y}{b} = 1 \). Final Answer:} \( \frac{x}{a} + \frac{y}{b} = 1 \).