Question

In Exercise 8.1.1, you learned the definition of direct and inverse variations, and then you practiced creating these variations. Fill in the blanks with SOMETIMES, ALWAYS, or NEVER to complete each sentence.

Direct variations are ____ linear and _____ go through the origin.

Inverse variations are ____ linear and _____ go through the origin.

Answer 1

Direct variations are __always_ linear and ___always__ go through the origin.

Inverse variations are _never___ linear and __never__ go through the origin.

• For inverse variation i.e y=k/x putting x=0 makes it undefined

Answer 2

Explanation:

• Direct variations are ALWAYS linear and ALWAYS go through the origin.

Because y = kx is linear function and y = 0 when x = 0

• Inverse variations are NEVER linear and NEVER go through the origin.

Because y = k/x is not a linear function and x is never zero as we can't divide by zero.