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 = 22 when a = -23. Which equation represents this direct variation between a and b?

Answer 1

Explanation:

In a direct variation, when two variables are related, one variable varies directly with the other if it can be expressed as their product, with a constant of proportionality.

Let's analyze the given information:

- Number b is located the same distance from 0 as another number a, but in the opposite direction.

- Number b varies directly with number a.

- When a = -23, b = 22.

We can express this direct variation relationship using an equation of the form y = kx, where y represents b, x represents a, and k is the constant of proportionality.

Using the given example values, we can substitute them into the equation and solve for k:

22 = k * (-23)

Dividing both sides of the equation by -23:

k = 22 / (-23)

Simplifying the expression:

k = -22/23

Now, we have the value of the constant of proportionality, k, which is -22/23.

Therefore, the equation representing the direct variation between a and b is:

b = (-22/23) * a