1986 AMC 12 Problem 2

Attempt Problem 2 of the 1986 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

If the line

L

in the

xy

-plane has half the slope and twice the

y

-intercept of the line

y=\frac23x+4,

then an equation for

L

y=\frac13x+8

y=\frac43x+2

y=\frac13x+4

y=\frac43x+4

y=\frac13x+2

Read the slope and intercept from

y=mx+b

Apply the two requested changes to the coefficient and constant separately

The original line has slope

\frac{2}{3}

and

y

-intercept

4.

Therefore

L

has slope

\frac{1}{3}

and

y

-intercept

8,

so its equation is

y=\frac13x+8.

Thus the correct answer is A.

Problem 2 in other years