A straight line makes positive intercepts on the coordinate axes whose sum is 5 . If the line passes through the point P(-3,4) then the equation of a line is

Step-by-step solution

Let the intercepts of the line on the x-axis and y-axis be a and b respectively. The equation of the line in intercept form is x a + y b = 1 . Given that a + b = 5 , we have b = 5 - a . Substituting this into the equation, we get x a + y 5 - a = 1 . Since the line passes through the point P(-3, 4) , we substitute x = -3 and y = 4 into the equation: -3 a + 4 5 - a = 1 Multiplying by a(5 - a) , we get -3(5 - a) + 4a = a(5 - a) . -15 + 3a + 4a = 5a - a^2 a^2 + 2a - 15 = 0 Factoring the quadratic equation: (a + 5)(a -