Determine whether the relation shown in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write an equation for the function.

x ] 10, 15, 20, 25
y ]1/2, 1/3, 1/4, 1/5

Question

Determine whether the relation shown in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write an equation for the function.

x ] 10, 15, 20, 25 
y ]1/2, 1/3, 1/4, 1/5

whpalmer4 · Answer

Test for indirect variation:  x*y = the same value for all values of x and y
Test for direct variation: y/x = the same value for all values of x and y

whpalmer4 · Answer

Once you've figured out whether it is direct or indirect variation, you'll either have

$$y = kx$$for direct variation, with $k=$ the same value you found when dividing y/x
or
$$xy = k$$for indirect variation, with $k=$ the same value you found when multiplying x*y

anonymous · Answer

Indirect variation since all the values for x and y were the same. (It did not pass direct variation since the valeus changed.)

I'm not sure how to write the equation tho......

whpalmer4 · Answer

Agreed that it is indirect variation, because the product of x and y is always 5.

That's how you write the equation:
$$xy=5$$

Or you can write one of the equivalent forms:
$$x=\frac{5}{y}$$$$y=\frac{5}{x}$$

whpalmer4 · Answer

I suppose there might be some situation in which it would be useful to write
$$\frac{xy}5=1$$perhaps some situation in which scaling the values was helpful.  I haven't ever seen it, but it is equivalent...

I would personally go with $xy=5$ or $y=\dfrac{5}{x}$

anonymous · Answer

I see thank you :)