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 3/4when a = –2 3/4. Which equation represents this direct variation between a and b?

Answer:The direct variation says that: [tex]y \propto x[/tex]Then the equation is of the form:[tex]y=kx[/tex] where k is the constant of Variation.As per the statement:A number b varies directly with the number a. i.e [tex]b \propto a[/tex]By definition of direct variation:[tex]b = ka[/tex]              .....[1]if [tex]b= 2\frac{3}{4}[/tex] and [tex]a=-2\frac{3}{4}[/tex] Substitute in [1] we get k;[tex]2\frac{3}{4}= k(- 2\frac{3}{4})[/tex] Divide both sides by [tex]2\frac{3}{4}[/tex] we get;1 = -kork = -1 ⇒equation becomes: b = -aTherefore, an equation represents this direct variation between a and b is:[tex]b = -a[/tex]