Determine If Each Function Listed Below Is Linear Or Non-Linear. Explain Your Thinking

EXIT TICKET

Determine if each function listed below is linear or non-linear. Explain your thinking.

1. A cell phone company charges a monthly fee of $50 for 300 minutes. Each additional minute costs $0.05.

Linear, because the equation would be y = 0.05x + 50 and there is a constant rate of change of 0.05.

2. A = s² Non-Linear, because the equation cannot be arranged to the form y = mx + b. It is in the form y = x². The x is being squared therefore each y value would have a positive and negative x value. Students could also use a table to determine pairs do not have the same rate of change (ie (0,0), (1,1), (2,4), (3,9) and y differences would be 1, 3, 5, etc.).

3. (-2, 8); (0, 7); (2, 6); (4, 5) Linear, because each input (x-coordinate) has a difference of 2 and each output (y-coordinate) has a difference of 1. The difference between each pair is constant.

Input Output 3 -7 7 -5 9 -1 10 0 4.

Non-Linear, because the difference between the pairs of inputs and outputs is not constant. (- 5 - -7/7 – 3 = ½ but 0 - -1/0 – 10 = -1/10).

5. Non-Linear because all pairs of points do not have the same slope or the same vertical intercept.