Y=3x to the 3rd 15. Is that a linear or non linear equation

Question

Y= 3x to the 3 power + 15 how do you find out if it's linear or non linear

Answer 1

Linear means that it is going in a straight line.

(1, 1), (2, 2) (3, 3) is an example of a straight line with a slope of 1. (For every 1 more to x, y is 1 more as well.)

(1, 2), (2, 4) (3, 6) is another example of a straight line with a slope of 2. (For every 1 more to x, y is 2 more.)

 

Let's ignore the +15 for a moment and take a look at the exponential, since that is the important part.

if we have x = 1, then y = 1 or (1, 1)

if x = 2, then y = 8, or (2, 8)

if x = 3, then y = 27, or (2, 27)

 

If you look at it, there is a difference between what's between x= 1 and 2, and an even bigger difference between x =2 and 3. As such, it is not a straight line and thus not linear.