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Solution


Q.

Consider the lines given by the equations y = (1/3)x + 5 and y = (1/3)x − 2. Which of the following statements are true regarding these lines

 

(i) They intersect in 1st quadrant.
(ii) They are parallel to each other.
(iii) They intersect at the point where x = −1.
(iv) They have different values of y at x = 0.
1 (i), (iii) and (iv)  
2 (i), (ii), (iii) and (iv)  
3 (ii) and (iv)  
4 (i) and (iv)  

Ans.

(3)

Here, a?/a? = (1/3)/(1/3) = 1, b?/b? = (−1)/(−1) = 1, c?/c? = 5/(−2).
The two lines are parallel (as a?/a? = b?/b? ≠ c?/c?). Therefore, they do not intersect.

At x = 0, y = (1/3)×0 + 5 = 5.
At x = 0, y = (1/3)×0 − 2 = −2.
Hence, statements (ii) and (iv) are correct