Question

Could you please help me with questions 36 & 37?

Answer 1

We have to determine if the functions are linear or not.

We can do this by rearranging the equations in this form:

`y=mx+b`

where m and b are constants.

NOTE: There are many ways to prove that a function is linear, but this is the easiest for this question.

36.

`\begin{gathered} x+(1)/(y)=7 \\ (1)/(y)=-x+7 \end{gathered}`

As this function can not be written in the form y=mx+b, then it is not linear.

37.

`\begin{gathered} (x)/(2)=10+(2y)/(3) \\ (x)/(2)-10=(2y)/(3) \\ (2y)/(3)=(1)/(2)x-10 \\ y=(3)/(2)((1)/(2)x-10) \\ y=(3)/(4)x-15 \end{gathered}`

This function is now in the form y=mx+b, where m=3/4 and b=-15. Then, this function is a linear function.

Answer:

36. Non-linear.

37. Linear.