Equation of a Straight Line

[Aman verma]

Q : What will be the equation of the straight line AB ?

I.The line passes through the point ( 3 , 4).

II.The line has intercepts on the axes such that their sum is 14.

[outreach]

answer should be C
option 1 would have been sufficient if we knew the slope and constant
4=3m+c

option 2
let the line be y=mx+c
y intercept is c
x intercept is c/m
c+c/m=14

solve the eq in option 1 and option 2 to get slope and constant.

[kstv]

eq of a st line y = mx+c
1) (x,y) is (3,4) m and c still 2 unknown
2) y intercept is c and x intercept is 14-c not sufficient but we know m = c/c-14
combine with 1)
4=(c/c-14)(3) + c
4(c-14) = 3c + c(c-14)
expressio c(c-14) is quadratic so 2 values
still not suff IMO E

[Fiver]

agree with E.
Both stmts combined we get c = 8 or c = 7 and thus the value of c and m will change in both cases.

[STEVEN SPIELBERG]

What's the OA ?

[Aman verma]

Sol: Let the equation of the line in the intercept form be : x/a + y/b = 1, where a and b are the intercepts on the axes.

From statement I. we get :3/a + 4/b = 1 since the line passes through point ( 3 , 4 ) .Not sufficient.

From statment II. we get : a + b = 14 or b = 14 - a. Not sufficient

Combining , we get : 3/a + 4/(14-a) = 1 => a = 6 , 7
so we get two equations : 4x + 3y = 24 and x + y = 7. Still not sufficient.

Hence, AnsE

[STEVEN SPIELBERG]

Thanks. I thought it was C .