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Question:

If a line intercepted between the coordinate axes is trisected at a point A(4,3), which is nearer to x-axis, then its equation is

3x+8y=36

4x-y=7

3x+2y=18

x+3y=13

Solution:

If the x-intercept of a line is h and its y-intercept is k, h+yk=1 represents the equation of that line. Thus, here point (4,3) divides the line joining points (h,0) (0,k) in the ratio 1:2 since the point is closer to x-axis. 1×0+2×h3=4 ⇒h=6 1×k+2×03=3 ⇒k=9 Equation of line is x6+y9=1 3x+2y=18.