# Maxine’s Rule – Graphing Inequalities

As a high emphasis topic on the TASC, it is likely that students will have to understand the graphs of linear inequalities in two variables (aka. a function). One type of question commonly used to assess this understanding is one where students are given a linear inequality and asked to choose which of four given graphs matches that function.

There are two versions of this activity/student handout included here for teachers to choose.

They both give students an inequality…

y ≥ ½ x + 7

… and a choice of four graphs.

Students who are working with the CUNY HSE Math Curriculum Framework in class will recognize the inequality as Maxine’s Rule from Unit 1. The difference between  the two has to do with the distractors.

“Distractors” are answers that are compelling but incorrect, based on common student mistakes – and they are all over the TASC.

The first version allows students to see how the shading works when looking at graphs of inequalities, specifically in the context of any prior discussions of Maxine’s Rule.

Here are the distractors and the answer:

• Choice A is the graph of y ≥  2( x – 7)
• Choice B is the graph of y  ≤ 2( x – 7)
• Choice C is the graph of y ½ x + 7
• Choice D is the correct answer – the graph of y ≥ ½ x + 7

The second version also allows students to see how the shading works when looking at graphs of inequalities. It also allows teachers to discuss the differences in the graphs of inequalities with >, < (dotted lines) versus  ≤, ≥ (solid line).

Here are the distractors and the answer:

• Choice A is the graph of y > ½ x + 7
• Choice B is the graph of y  ≤ ½ x + 7
• Choice c is the graph of y < ½ x + 7
• Choice D is the correct answer – the graph of y ≥ ½ x + 7

Both versions ask students to explain why they choose the answer they choose. This is a great opportunity to get students in the habit of putting an input into the function, getting an output and seeing if the ordered pair is on the graph. For example, in version 1, putting a 0 into the given inequality (Maxine’s Rule) tells you that when x is 0, y ≥ 7. That allows you to eliminate choices A and B.

BONUS

As a bonus exploration, I am including what I call, “The Cone Version.” This has the graph of both of Maxine’s Rules (her rule for determining the youngest person she is willing to date and her rule for determining the oldest person she is willing to date, based on her current age). Including both inequalities creates a double-shaded “cone” displaying the dating age range for people aged 14-80. I think this would be a really rich activity to use as a Notice Wonder.

NB: Though this activity references the Maxine’s Rule activity in Unit 1 of the CUNY Framework, it is probably more appropriate to do this activity after doing Unit 2, where students are introduced to the graphing representation of a function.