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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.

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Solution

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



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