A2 – Section 2.8 Date______
Inequalities in Two Variables
Inequality in two variables: any function using x and y that has an ______instead of an equal sign to relate the two sides
· Usually, there are ______solutions to inequalities in two variables, which will be ordered pairs.
· You will need to ______half of the graph, called a half-plane, to show all of the solutions.
· You will need to consider if the boundary line should be included in the solution graph. (You’ll use a solid line if the boundary line is included,)
Ex 1 Check to see if the following ordered pairs are solutions of 5x + 8y 23.
a) (-2, 6) / b) (3, 1) / c) (4, -5)Boundary lines:
· ______boundary lines mean that the boundary line is included in the solution set. Use a solid line for or .
· ______boundary lines mean that the boundary line is NOT included in the solution set. Use a dashed line for < or >.
a) (2, -4) / b) (3, 4)c) (5, 0) / d) (1, 3)
Graphing Inequalities in Two Variables:
· Graph the boundary line of the inequality. Remember to use a ______line for < or > and a ______line for or .
· Test a point that is NOT on the boundary line, and decide if it is a solution to the inequality. If it is a solution, ______the half-plane containing that point. If it is NOT a solution, ______the other half-plane.
Ex 3 Graph the following inequalities.
a) y -⅜x + 5 / b) 4x – 7y > 28c) x > 6
/ d) y < -5
Ex 4 The memory card of your digital camera has 256 megabytes of memory. Each photo uses either 1 megabyte or 2 megabytes, depending on low or high resolution photos. Write an equation that models the number of photos that can be stored on the card when you take photos of both resolutions. What are three possible solutions?
a) Equation? / b) Solutions?