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?

Answer 1

Direct variation means b = k·a for some constant k. Because b is the same distance from 0 as a but opposite in sign, b = −a. (So k = −1; e.g., if a = −2 then b = 2, and if a = 3/4 then b = −3/4.)