Question

Which equation does NOT show direct variation?

12y = x
y = ½x
y + 20 = x + 20
y = 34x + 2

Answer 1

direct variation means you can write the equation as
y = k x
where k is a number (such as a fraction, or integer, etc)

for the first equation
12y= x
if you divide both sides by 12 you will get
\[ y = \frac{1}{12} x\]

the second equation is
\[ y= \frac{1}{2}x\]

the 3rd equation
y+20= x+20
if you add -20 to both sides you get
y+20-20 = x+20-20 or
y+0=x+0 or
y= x
which can be written as
\[ y = 1 x \]