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, [tex] y = xk [/tex], where k is a constant. Thus,
[tex] \frac{y}{x} = k [/tex]
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, [tex] \frac{0.50}{1} = 0.5 [/tex]
k = 0.5.
If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into [tex] \frac{y}{x} = k [/tex], should give us the same constant if proportionality.
Let's check:
When x = 2, and y = 1:
[tex] \frac{y}{x} = k [/tex],
[tex] \frac{1}{2} = 0.5 [/tex],
When x = 3, y = 1.5:
[tex] \frac{1.5}{3} = 0.5 [/tex],
When x = 5, y = 2.50:
[tex]\frac{2.5}{5} = 0.5[/tex],
The constant of proportionality is the same. Therefore, the relationship forms a direct variation.
