Question

Equation of the straight line making equal intercepts on the axes and passing through the point $(2,4)$ is
A. $4x-y-4=0$
B. $2x+y-8=0$
C. $x+y-6=0$
D. $x+2y-10=0$

Answer 1

Hint: In this question, we need to find the equation of a straight line that makes equal intercepts on the axes and passes through the given point. In order to find this, we use the standard form of a straight line called the intercept form. By the given condition, we can easily evaluate the required equation.

Formula used: The equation of a line with two intercepts on the $x$ and $y$ axes is
$\dfrac{x}{a}+\dfrac{y}{b}=1$
Where $a$ and $b$ are the intercepts on the $x$ and $y$ axes respectively.

Complete step by step solution: Given that, the required equation has two intercepts.
So, consider the equation as
$\dfrac{x}{a}+\dfrac{y}{b}=1\text{ }...(1)$
Since it is given the equation has equal intercepts.
Then, we can write $a=b$
So, equation (1) is rewritten as
$\dfrac{x}{a}+\dfrac{y}{a}=1$
On simplifying, we get
$\begin{align}
  & \dfrac{x}{a}+\dfrac{y}{a}=1 \\
 & x+y=a\text{ }...(2) \\
\end{align}$
The obtained equation at (2) passes through the point $(2,4)$.
So, substituting the given point in (2), we get
$\begin{align}
  & \Rightarrow x+y=a \\
 & \Rightarrow 2+4=a \\
 & \therefore a=6 \\
\end{align}$
Thus, the equation is
 $\begin{align}
  & x+y=6 \\
 & \Rightarrow x+y-6=0 \\
\end{align}$

Thus, Option (C) is correct.

Note: Here we need to remember the given condition that the intercepts of the required equation are equal. By this, we are able to calculate the intercept value and then we can frame the equation.