The variables x an y vary directly. When x=13, y=52. Which equation correctly relates x and y?

The equation which correctly relates x and y is y = 4x

Step-by-step explanation:

The equation of the direct variation is y = k x, where

∵ The variables x and y vary directly

→ Use the form of the equation above

∴ y = k x

∵ When x = 13, y = 52

→ That means the initial values of x and y are 13 and 52

∴ x = 13 and y = 52

→ Substitute them in the equation above to find k

∵ 52 = k (13)

∴ 52 = 13k

→ Divide both sides by 13

∴ 4 = k

∴ The value of k is 4

→ Substitute it in the equation

∴ y = 4x

∴ The equation which correctly relates x and y is y = 4x

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