Question

The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:

• A. \( x + y = 5 \)
• B. \( 3x + 2y = 12 \)
• C. \( 2x + 3y = 12 \)
• D. \( 5x + 5y = 25 \)

Hint:

Lines with equal intercepts on x- and y-axes follow the form: \[ x + y = \text{constant} \] Use the given point to find that constant.

Answer 1

The Correct Option is A

Step 1: General equation of a line with equal intercepts on both axes. The line making equal intercepts \( a \) on x- and y-axis has the form: \[ \frac{x}{a} + \frac{y}{a} = 1 \Rightarrow \frac{x + y}{a} = 1 \Rightarrow x + y = a \] Step 2: Use the given point to find the intercept \( a \). Substitute point \( (2, 3) \) into \( x + y = a \): \[ 2 + 3 = a \Rightarrow a = 5 \Rightarrow \text{So the line equation is } x + y = 5 \] Step 3: Verify the line passes through (2, 3). \[ x + y = 2 + 3 = 5 \Rightarrow \text{True} \]