Question

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2a equals negative 2 and StartFraction 3 Over 4 EndFraction. when a = –2a equals negative 2 and StartFraction 3 Over 4 EndFraction.. Which equation represents this direct variation between a and b?

b = –a
–b = –a
b – a = 0
b(–a) = 0

Answer 1

Based on the information given, number \( b \) is located the same distance from 0 as number \( a \), but in the opposite direction. This implies that \( b \) is the negative of \( a \), so we can express this relationship as:

\[
b = -a
\]

This equation indicates that \( b \) and \( a \) vary directly in the sense that when \( a \) increases or decreases, \( b \) does so in the opposite direction.

Therefore, the correct equation that represents the direct variation between \( a \) and \( b \) is:

\[
b = -a
\]