Track / Stage 3 / 9 of 260 #9 of 1964

Problem 9

AMC 10/12, early questions

Algebra Difficulty 3.0 Find the answer

A line $l$ passes through point P(1, 4) and has equal intercepts on both coordinate axes. What is the equation of line $l$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

When the line passes through the origin, its equation is $y=4x$ , which can be rewritten as $4x-y=0$ .

When the line does not pass through the origin, let's assume the equation of the line is $x+y=k$ . Substituting point (1, 4) into this equation gives $k=5$ .

Therefore, the equation of the line is $x+y-5=0$ .

In summary, the equations of the line sought are $4x-y=0$ or $x+y-5=0$ .

Hence, the answer is $\boxed{4x-y=0 \text{ or } x+y-5=0}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.