Question

A line has slope -3/4 , positive y-intercept and forms a triangle of area 24 sq. unit its with coordinate axes. Then, the equation of the line is

(A)  3x + 4y + 24 = 0

(B)  3x + 4y - 24 = 0

(C)  3x + 4y - 25 = 0

(D)  3x + 4y + 25 = 0

Answer 1

Correct option  (B)  3x + 4y - 24 = 0

Explanation :

Let the line be

y = (-3/4) x + c

so that the intercepts on the x and y axes, respectively, are 4c/3 and c. Therefore, the area of the triangle

Since y-intercept is positive, the value c is 6 and the equation of the line is 3x + 4y - 24 = 0.