Question

The intercepts of a line with coordinate axes are equal. If the line passes through (2, 3), then its equation is

• A. 2x+3y=5
• B. x+y=5
• C. 5x+5y=1
• D. x+y=6
• E. 3x+2y=5

Answer 1

The Correct Option is B

The general equation of a line whose intercepts with the coordinate axes are equal is: \[ \frac{x}{a} + \frac{y}{a} = 1 \] where $a$ is the intercept on both axes. Simplifying this, we get the equation of the line: \[ x + y = a \] Since the line passes through the point $(2, 3)$, we substitute these values into the equation: \[ 2 + 3 = a \] Thus, $a = 5$. Therefore, the equation of the line is: \[ x + y = 5 \]

The correct option is (B) : \(x+y=5\)

Answer 2

Let the intercepts of the line with the coordinate axes be \(a\). Then the line passes through the points \((a, 0)\) and \((0, a)\).

The equation of a line in intercept form is \(\frac{x}{a} + \frac{y}{b} = 1\), where \(a\) is the x-intercept and \(b\) is the y-intercept.

Since the intercepts are equal, we have \(\frac{x}{a} + \frac{y}{a} = 1\), which simplifies to \(x + y = a\).

The line passes through the point \((2, 3)\). Substituting this point into the equation, we get:

\(2 + 3 = a\)

\(a = 5\)

Therefore, the equation of the line is \(x + y = 5\).