Question

If the line $2x + 5y = k$passes through origin then $k = $
A. $0$
B. $1$
C. \[ -1\]
D. $2$

Answer 1

Hint: If any general point say $(a,b)$passes through any given straight line then that point satisfy the given straight line
Say: General equation of straight line is $ax + by + c = 0$
If $(x,y)$,point is passing through above straight line, then $({x_1},{y_1})$will satisfy above straight line $ax + by + c = 0$
i.e. putting the value of $({x_1},{y_1})$in straight line, we will get
$a{x_1} + b{y_1} + c = 0$

Complete step-by-step answer:
In general, therefore, the equation y = mx represents a straight line passing through the origin with gradient m. The equation of a straight line with gradient m passing through the origin is given by y = mx.
Here, given straight line is $2x + 5y = K$
It is given that the line$2x + 5y = K$passes through origin,
It means line $2x + 5y = K$, will satisfy the origin point i.e. $(0,0)$
So, putting $(0,0)$in above line $2x + 5y = K$,
We will get
$2(0) + 5(0) = K$
$ \Rightarrow 0 + 0 = K$
$ \Rightarrow K = 0$
Thus, the required value of $K$ for which the given line $2x + 5y = K$ passes through origin is $K = 0$
So, the correct answer is “Option A”.

Note: Any straight line say $ax + by + c = 0$ passes through origin will satisfy the point $(0,0)$when $(0,0)$is put into the line
i.e. $a(0) + b(0) + c = 0$
$ \Rightarrow C = 0$. Hence the value of \[C\]will be zero.
So in case of competitive exams one can directly write the value of zero.