Question

Assertion: x + y = 5 is the equation of a line passing through the origin.
Reason: y = mx is the equation of a line passing through the origin.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(d) Assertion is false and Reason is true.
Given equation: $x+y=5$
Or, $y=5-x$
When
$x=1,y=5-1=4$
$$\begin{gathered} x=2,y=5-2=3 \\ x=3,y=5-3=2 \\ x=4,y=5-4=1 \\ x=5,y=5-5=0 \end{gathered}$$
Thus, we get the following table:

$\text{x}$	1	2	3	4	5
$y$	4	3	2	1	0

Plot the points $(1,4),(2,3),(3,2),(4,1)$ and $(5,0)$. Join these points and extend them in both the directions.
We get a line that does not pass through the origin.
Moreover, we know that $y=mx$ is the equation of the line passing through the origin.
So, Assertion (A) is false and Reason (R) is true.