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 when a = –2. which equation represents this direct variation between a and b?

The equation is b = -a

Step-by-step explanation:

Given,

The number b varies directly with the number a,

That is, we can write,

b ∝ a

⇒ b = ka

Where k is the constant of proportionality,

Given, if b = 2 then a = -2,

By substituting the value,

2 = k(-2)

⇒ k = -1

Hence, the equation that represents the direct variation between a and b is,

b = -a

1,8,15,22,29,36,43,50

step-by-step explanation:

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.