Question

Function Q: y =1/3x + 2 Identify function Q as linear or nonlinear. State a reason why it is linear or nonlinear.

Answer 1

A linear function is written in slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

So any function of this shape, is a linear function, such that when graphed it is a straight line.

In this case, the function you wrote is:

Q: y = 1/3x + 2

Now, if the function is exactly what you wrote, then x is in the denominator:

y = 1/(3*x) + 2

Clearly, this is different than the general linear equation you can see above (here the variable is in the denominator) then in this case Q is non-linear.

If instead, the actual function Q is:

Q: y = (1/3)*x + 2

Then this is a linear equation, where the slope is 1/3 and the y-intercept is 2.