University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

351

Pages:

3
Author:

Aryan Henderson

5.6 | Graphing Linear Inequalities in 2 Variables Review Equation: y = -2/3x + 1 Equation: 3y - x = 6 -> 3y = x + 6 -> y = 1/3x + 2 Vocabulary and Rules Inequality: less than (<) greater than (>) less than or equal to (≤) greater than or equal to (≥) One-Variable Graph x < 3 x > 3 x ≤ 3 x ≥ 3 Two-Variable Graph y < mx + b y > mx + b y ≤ mx + b y ≥ mx + b Graphing Inequalities Step 1: Using the y = mx + b (make it happen) Step 2: Start with "b" Step 3: Follow the slope (down 2, right 3) Step 4: Decide type of line (dotted or solid) Step 5: Decide your shade zone (using a Test Point (0, 0)) Example: 3y ≤ -2x + 12 3(0) ≤ -2(0) + 12 0 ≤ 12 (True) In Exercises 1-6, tell whether the ordered pair is a solution of the inequality. x + y 1 > 5; (3, 2) 3 + 2 > 5 5 > 5 False No x - y ≥ 2; (5, 3) 5 - 3 ≥ 2 2 ≥ 2 True Yes x + 2y ≤ 4; (-1, 2) -1 + 2(2) ≤ 4 -1 + 4 ≤ 4 3 ≤ 4 True Yes 5x + y < 7; (2, -2) 5(2) + (-2) < 7 10 - 2 < 7 8 < 7 False No 3x - 4y > 6; (-1, -1) 3(-1) - 4(-1) > 6 -3 + 4 > 6 1 > 6 False No -x - 2y ≥ 5; (-2, -3) -(-2) - 2(-3) ≥ 5 2 + 6 ≥ 5 8 ≥ 5 True Yes In Exercises 7-18, graph the inequality in a coordinate plane. y < 4 (Graph of a horizontal line at y = 4, shaded below the line) x > -1 (Graph of a vertical line at x = -1, shaded to the right of the line) x ≥ 3 (Graph of a vertical line at x = 3, shaded to the right of the line) x ≤ 1 (Graph of a vertical line at x = 1, shaded to the left of the line) y ≤ -2 (Graph of a horizontal line at y = -2, shaded below the line) x ≥ -2 (Graph of a vertical line at x = -2, shaded to the right of the line)