Question

Part A: A graph passes through the points (0, 2), (2, 6), and (3, 12). Does this graph represent a linear function or a non-linear function? Explain your answer in words.

Part B: Write one example of a linear function and one example of a non-linear function. (Use x and y as the variables)

Answer 1

part A: long method: use the slope formula to calculate the slope between (0,2) and (2,6)

then use the slope formula to calculate the slope between (2,6) and (3,12)

shorter/more intuitive method: going from (0,2) to (2,6), x increases by 2 and y increases by 4 (from 2 to 6). assuming linearity, that means for every increase of 1 in x, y increases by 2. now, going from (2,6) to (3,12) is that still true?

Answer 2

part B: your linear function should take the form y = mx + b (fill in m and b values of your choosing). notice how the exponent on x is 1.

for a non-linear function, the exponent on x can be anything but 1 (0 is also excluded since x^0 = 1 which just gives y = a constant)