Question

Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.

x | 1 | 2 | 5 | 10
------------------------
y | 6 | 12 | 30 | 60

ps. sorry table is so bad

Answer 1

Answer: Direct Variation

The equation is y = 6x

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Reason:

Divide each y value over its corresponding x value

• column one: y/x = 6/1 = 6
• column two: y/x = 12/2 = 6
• column three: y/x = 30/5 = 6
• column four: y/x = 60/10 = 6

Each time we get the same result. This suggests that y/x = k where k is the constant of proportionality. That equation rearranges into y = kx to show we have a direct variation.

The equation is y = 6x since k = 6

Side note: an inverse variation happens when we multiply the x,y values and get the same result each time.