2-3-3 Graphing Linear Inequalities Act 1

​2-3-3 Graphing Linear Inequalities

​1a.) If she scores 6 two-point shots and 2 three-point shots, will Bena meet her points-per-game average?


1b.) If she scores 7 two-point shots and 2 three-point shots, will Bena meet her points-per-game average?


1c.) If she scores 7 two-point shots and 4 three-point shots, will Bena meet her points-per-game average?

Multiple Choice

2.) Write an equation to represent the number of two-point shots and the number of three-point shots that total 20 points. Let x be the number of 2-point and y be the number of 3-point.

• x + y = 20

• 2x + 3y =20

• 3x + 2y = 20

• y = 2x + 20

​3.) Graph the equation you wrote on the coordinate plane. Let your x-axis be the number of 2-point shots and your y-axis be the number of 3-point shots.

​3.) Graph the equation you wrote on the coordinate plane. Let your x-axis be the number of 2-point shots and your y-axis be the number of 3-point shots.

​Plot the following points:
1a: 6 two-point shots and 2 three-point
1b: 7 two-point shots and 2 three-point shots
1c: 7 two-point shots and 4 three-point shots

Multiple Choice

4a-b.) How can you rewrite the equation you wrote in Question 2 to represent that Bena must score at least 20 points per game? Write an inequality in two variables that represents this problem situation?

• $$2x\ +\ 3y>20$$

• 2x + 3y $$\ge$$ 20

• $$2x\ +\ 3y\ <20$$

• $$2x\ +\ 3y\le20$$

​5.) Complete the table of values. Then, add the ordered pairs in the table to the graph in Question 3. If the number of total points scored does not meet or exceed Bena’s points-per-game average, use an X to plot the point. If the number of total points scored meets or exceeds Bena’s points-per-game average, use a dot to plot the point.

​5.) Complete the table of values. Then, add the ordered pairs in the table to the graph in Question 3. If the number of total points scored does not meet or exceed Bena’s points-per-game average, use an X to plot the point. If the number of total points scored meets or exceeds Bena’s points-per-game average, use a dot to plot the point.

6.) What do you notice about your graph?

7.) What can you interpret about the solutions of the inequality from the graph?

8.) Choose a different ordered pair located above the line and a different ordered pair that is located below the line. How do these points confirm your interpretation of the situation? Explain your reasoning.

9.) Shade the side of the graph that contains the combinations of shots that are greater than or equal to Bena’s points-per-game average.  

10.) How do the solutions of the linear equation 2x + 3y = 20 differ from the solutions of the linear inequality 2x + 3y ≥ 20?

11.) Does the ordered pair (6.5, 5.5) make sense as a solution in the context of this problem situation? Explain why or why not.