Question

The table below shows the amount paid for different numbers of items. Determine if this relationship forms a direct variation. Verify your answer.

Answer 1

Answer/Step-by-step explanation:

Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.

The ratio of between y-variable and x-variable would be constant.

Direct variation can be represented by the equation, $y = xk$, where k is a constant. Thus,

$\frac{y}{x} = k$

From the table given, it seems, as x increases, y also increases. Let's find out if there is a constant of proportionality (k).

Thus, ratio of y to x, $\frac{0.50}{1} = 0.5$

k = 0.5.

If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into $\frac{y}{x} = k$, should give us the same constant if proportionality.

Let's check:

When x = 2, and y = 1:

$\frac{y}{x} = k$,

$\frac{1}{2} = 0.5$,

When x = 3, y = 1.5:

$\frac{1.5}{3} = 0.5$,

When x = 5, y = 2.50:

$\frac{2.5}{5} = 0.5$,

The constant of proportionality is the same. Therefore, the relationship forms a direct variation.