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A line passes through (3, 4) and cuts off equal positive intercepts on the two axes. What is its equation?

Competition practiceGeometry

A $x + y = 7$
B $x - y + 1 = 0$
C $x + y = 12$
D $4 x - 3 y = 0$

Step-by-Step Solution

With equal intercepts a, the line is

\frac{x}{a} + \frac{y}{a} = 1

, i.e.

x + y = a

. Since (3, 4) lies on it,

a = 7

.

Answer: A)

x + y = 7

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