on a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite…

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 = 2\\frac{3}{4} when a = -2\\frac{3}{4}. which equation represents this direct variation between a and b?\no b = -a\no -b = -a\no b - a = 0\no b(-a) = 0

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 = 2\\frac{3}{4} when a = -2\\frac{3}{4}. which equation represents this direct variation between a and b?\no b = -a\no -b = -a\no b - a = 0\no b(-a) = 0

Answer

Answer:

A. $b=-a$

Explanation:

Step1: Understand the problem

A number $b$ is opposite of $a$ on number - line.

Step2: Analyze direct - variation

If two numbers are the same distance from 0 but in opposite directions, then $b=-a$. For example, when $a = - 2\frac{3}{4}$, $b=2\frac{3}{4}$, which satisfies $b=-a$.

Step3: Check other options

  • Option B: $-b=-a$ simplifies to $b = a$, which is incorrect as $a$ and $b$ are opposites.
  • Option C: $b - a=0$ simplifies to $b = a$, incorrect.
  • Option D: $b(-a)=0$ means either $b = 0$ or $a = 0$ or both, which is not the correct relationship.