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.

$\begin{gathered} x+\frac{1}{y}=7 \\ \frac{1}{y}=-x+7 \end{gathered}$

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

37.

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

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.