The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1 is

Answer

`(x)/(2)+(y)/(-3) = 1 " and " (x)/(-2) + (y)/(1) = 1`

Explanation

Let a and b be the intercepts on the axes. Then the equation of the line is
`(x)/(a) + (y)/(b) = 1 " "(1)`
Since (1) passes through (4,3), we get
`(4)/(a) + (3)/(b) = 1 " "(2)`
Also, given that
`a + b = -1 " "(3)`
From (3), we get
`b = -1-a " "(4)`
Putting in (2), we get
`(4)/(a)+ (3)/(-1-a) = 1`
` "or " -4-4a+3a = -a-a^(2)`
` "or " a^(2) = 4`
` "or " a = +-2`
When a = 2, then from (4), b = -1-2 = -3
and when a = -2, b=-1+2=1
Therefore, the line is
`(x)/(2) + (y)/(-3) = 1" and "(x)/(-2) + (y)/(1) = 1`