Investigation: Graphing Linear Inequalities in Two Variables

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Graphing Linear Inequalities in Two Variables

Sir Purrs-a-Lot and Honeycomb are a pair of domestic cats. Let \(s\) be the weight of Sir Purrs-a-Lot and let \(h\) be the weight of Honeycomb.

The inequalities \(s \gt h\) and \(s \lt h\) can be used to compare the weights of the cats.

1. Complete the tables by choosing pairs of values that make each inequality true. (Use values of \(25\) or less in these tables.)
   
   
   
   

   \(s \gt h\)
   \(s\)	\(h\)

   
   

   
   

   \(s \lt h\)
   \(s\)	\(h\)

   
   
   
   
2. Plot the ordered pairs from your tables. Use one colour or symbol for \(s \gt h\) and a different colour or symbol for \(s \lt h\).
   
   
   
   
3. Describe the arrangement of the two groups of points.
   
   
   
4. On your graph, draw the line representing \(s = h\). How is this equation related to the original inequalities? What does this line represent on the graph?
   
   
   
5. Suppose Sir Purrs-a-Lot and Honeycomb like to sleep together on a shelf that has a weight rating of \(40 \thinspace \rm{lbs}\). Write an inequality representing the weights the cats can be and still sleep on the shelf safely.
   
   
   
6. Complete the first table by choosing values for \(s\) and \(h\) that make the inequality from part 5 true. Complete the second table using values that make the inequality false.
   
   
   
   
   

   \(s\)	\(h\)

   
   

   \(s\)	\(h\)

   
   
7. Plot the ordered pairs from your tables. Use one colour or symbol when your inequality is true and a different colour or symbol when your inequality is false.
   
   
   
   
8. Describe the arrangement of the two groups of points.
   
   
   
9. Rewrite your inequality, replacing the inequality symbol with an equal sign, and graph the corresponding line on the grid used for part 7. What does this line represent on the graph?