In the xy-plane, how many straight lines whose x-intercept is a prime number and whose y-intercept is a positive integer pass through the point (4,3)?

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

The line `(x)/(p) +(y)/(q) =1`, where 'p' is a prime and 'q' is a positive integer, passes through (4,3).
`:. (4)/(p) +(3)/(q) =1`
`:. q = (3p)/(p-4) =3+(12)/(p-4)`
Since, q is a positie integer, `p gt 4` and `(p-4)` divides 12, there are only two such prime numbers,
`p = 5` and `p = 7`