6 5 Solving Linear Inequalities Warm Up Graph

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

6 -5 Solving Linear Inequalities Learning Target Students will be able to: Graph and solve linear inequalities in two variables. Holt Algebra 1

6 -5 Solving Linear Inequalities Tell whether the ordered pair is a solution of the inequality. (– 2, 4); y < 2 x + 1 4 2(– 2) + 1 4 – 4 + 1 4 < – 3 (– 2, 4) is not a solution. Holt Algebra 1

6 -5 Solving Linear Inequalities (3, 1); y > x – 4 y>x− 4 1 3– 4 1> – 1 (3, 1) is a solution. Holt Algebra 1

6 -5 Solving Linear Inequalities a. (4, 5); y < x + 1 b. (1, 1); y > x – 7 y<x+1 y>x– 7 1 1– 7 5 4+1 5 < 5 (4, 5) is not a solution. Holt Algebra 1 1 > – 6 (1, 1) is a solution.

6 -5 Solving Linear Inequalities 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. Holt Algebra 1

6 -5 Solving Linear Inequalities Holt Algebra 1

6 -5 Solving Linear Inequalities Graphing Linear Inequalities Step 1 Solve the inequality for y (slopeintercept form). Step 2 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >. Shade the half-plane above the line for y > Step 3 or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer. Holt Algebra 1

6 -5 Solving Linear Inequalities Graph the solutions of the linear inequality. y 2 x – 3 Check y 2 x – 3 0 2(0) – 3 0 – 3 Holt Algebra 1

6 -5 Solving Linear Inequalities Helpful Hint The point (0, 0) is a good test point to use if it does not lie on the boundary line. Holt Algebra 1

6 -5 Solving Linear Inequalities Graph the solutions of the linear inequality. 5 x + 2 y > – 8 Check 0 (0) – 4 0 > – 4 Holt Algebra 1

6 -5 Solving Linear Inequalities Graph the solutions of the linear inequality. 2 x – y – 4 > 0 Check Holt Algebra 1

6 -5 Solving Linear Inequalities Graph the solutions of the linear inequality. Check y≥ 0 Holt Algebra 1 x+1 (0) + 1 0 0+1 0 ≥ 1

6 -5 Solving Linear Inequalities 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. Holt Algebra 1

6 -5 Solving Linear Inequalities Remember, Ada can only use whole numbers for x and y. # of bracelets Solve for y and graph. In Algebra 2 we will determine which of those points maximizes profit! Holt Algebra 1 # of necklaces

6 -5 Solving Linear Inequalities Write an inequality to represent the graph. Holt Algebra 1

6 -5 Solving Linear Inequalities Write an inequality to represent the graph. Holt Algebra 1