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Condition for Two Lines to Be Parallel

Consider the ...

Question

Consider the equation of the line : $\frac{2 x - 1}{3} - \frac{y - 2}{5} = 0$ . Which of the following is correct?

A

x

- axix at

(\frac{1}{10}, 0)

;

y

-axis at

(0, \frac{1}{3})

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B

x

- axix at

(\frac{1}{10}, 0)

;

y

-axis at

(0, - \frac{1}{3})

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C

x

- axix at

(- \frac{1}{10}, 0)

;

y

-axis at

(0, - \frac{1}{3})

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D

x

- axix at

(- \frac{1}{10}, 0)

;

y

-axis at

(0, \frac{1}{3})

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Solution

The correct option is C $x$ - axix at $(- \frac{1}{10}, 0)$ ; $y$ -axis at $(0, \frac{1}{3})$
$T h e g i v e n e q u a t i o n i s \frac{2 x - 1}{3} - \frac{y - 2}{5} = 0 ⟹ y = \frac{10 x + 1}{3} H e r e x i s t h e i n d e p e n d e n t v a r i a b l e . W e a s s i g n a t l e a s t a n y 3 v a l u e s o f x a n d o b t a i n t h e c o r r e s p o n d i n g v a l u e s o f y . x = - 4 ⟶ y = - 13, x = 2 ⟶ y = 7, x = 5 ⟶ y = 17. S o t h e o r d e r e d p a i r e s o f v a l u e s o f (x, y) = (- 4, - 13), (2, 7) & (5, 17) . N o w w e p l o t t h e m o n a g r a p h . F r o m t h e g r a p h t h e p o i n t o f i n t e r s e c t i o n w i t h t h e Y - a x i s i s (0, b) = (0, \frac{1}{3}) a n d t h e p o i n t o f i n t e r s e c t i o n w i t h t h e X - a x i s i s (a, 0) = (- \frac{1}{10}, 0) (e x p a n d t h e g r a p h a r o u n d t h e o r i g i n e) A n s - O p t i o n D .$

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