Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0 3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2

Learning Target Students will be able to: Graph and solve linear inequalities in two variables.

Tell whether the ordered pair is a solution of the inequality. (–2, 4); y < 2x + 1 y < 2x + 1 4 2(–2) + 1 4 –4 + 1 4 –3 <  (–2, 4) is not a solution.

(3, 1) is a solution.  (3, 1); y > x – 4 y > x − 4 1 3 – 4 1 3 – 4 1 – 1 >  (3, 1) is a solution.

  a. (4, 5); y < x + 1 b. (1, 1); y > x – 7 y < x + 1 5 4 + 1 5 5 < 1 1 – 7 > 1 –6   (4, 5) is not a solution. (1, 1) is a solution.

A linear inequality describes a region of a coordinate plane called a half-plane. All points in the region are solutions of the linear inequality. The boundary line of the region is the graph of the related equation.

Graphing Linear Inequalities Step 1 Solve the inequality for y (slope-intercept form). Step 2 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >. Step 3 Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.

 Graph the solutions of the linear inequality. y  2x – 3 Check y  2x – 3 0 2(0) – 3 0 –3  

The point (0, 0) is a good test point to use if it does not lie on the boundary line. Helpful Hint

 Graph the solutions of the linear inequality. 5x + 2y > –8 Check 0 (0) – 4 0 –4 > 

Graph the solutions of the linear inequality. 2x – y – 4 > 0 Check

 Graph the solutions of the linear inequality. Check y ≥ x + 1 0 (0) + 1 0 0 + 1 0 ≥ 1 

Ada has at most 285 beads to make jewelry Ada has at most 285 beads to make jewelry. A necklace requires 40 beads, and a bracelet requires 15 beads. Write a linear inequality to describe the situation. Let x represent the number of necklaces and y the number of bracelets.

Solve for y and graph. # of bracelets Remember, Ada can only use whole numbers for x and y. In Algebra 2 we will determine which of those points maximizes profit! # of necklaces

Write an inequality to represent the graph.

Write an inequality to represent the graph.