If P(3,4) is the mid-point of a line segment between the axes, then what is the equation of the line ?

Explanation

Let the intercepts on the x and y axes be a and b respectively. The coordinates of the endpoints are (a, 0) and (0, b). The midpoint is (\frac{a}{2}, \frac{b}{2}) = (3, 4), which implies a=6 and b=8. The equation of the line is \frac{x}{6} + \frac{y}{8} = 1 \implies 4x + 3y = 24, or 4x + 3y - 24 = 0.

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