the table below shows the amount paid for different numbers of items. determine if this relationship forms a…

Explanation:

Step1: Recall the formula for direct variation

For direct variation, the formula is (y = kx), where (k) is the constant of variation. We can also check if (\frac{y}{x}) is constant for all pairs ((x,y)) in the table.

Step2: Calculate (\frac{y}{x}) for each pair

• When (x = 1) and (y=50), (\frac{y}{x}=\frac{50}{1}=50)
• When (x = 2) and (y = 100), (\frac{y}{x}=\frac{100}{2}=50)
• When (x = 3) and (y=150), (\frac{y}{x}=\frac{150}{3}=50)
• When (x = 5) and (y = 250), (\frac{y}{x}=\frac{250}{5}=50)

Since (\frac{y}{x}) is a constant ((k = 50)) for all values of (x) and (y) in the table, the relationship forms a direct variation.

Answer:

The relationship forms a direct variation. The constant of variation (k = 50) as (\frac{y}{x}=50) for all pairs ((x,y)) in the table.