Algebra 1 Section 5.6 Worksheet Determine which ordered pairs are part of the solution set for each inequality. 1. 3x + y ≥ 6, {(4, 3), (–2, 4), (–5, –3), (3, –3)} 2. y ≥ x + 3, {(6, 3), (–3, 2), (3, –2), (4, 3)} 3. 3x – 2y < 5, {(4, –4), (3, 5), (5, 2), (–3, 4)} Graph each inequality. 4. 2y – x < –4 5. 2x – 2y ≥ 8 6. 3y > 2x – 3 Use a to solve each inequality. 7. –5 ≤ x – 9 8. 6 > x + 5 9. > –2 x +
b) Write an equation in slope-intercept form for the line that passes through (4, 7) and is perpendicular to the graph of . 4.4 Textbook Homework Algebra 1 Section 4.4 Worksheet an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation. 1. (3, 2), y = x + 5 2. (–2, 5), y = –4x + 2 3. (4, –6), y = x + 1 4. (5, 4), y = x – 2 5. (12, 3), y = x + 5 6. (3, 1), 2x + y = 5 7. (–3, 4), 3y = 2x – 3 8. (–1, –2), 3x – y = 5 9. (–8, 2), 5x – 4y = 1 10. (–1, –4), 9x + 3y = 8 11. (–5, 6), 4x + 3y = 1 12. (3, 1), 2x + 5y = 7 Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation. 13. (–2, –2), y = x + 9 14. (–6, 5), x – y = 5 15. (–4, –3), 4x + y = 7 16. (0, 1), x + 5y = 15 17. (2, 4), x – 6y = 2 18. (–1, –7), 3x + 12y = –6 19. (–4, 1), 4x + 7y = 6 20. (10, 5), 5x + 4y = 8 21. (4, –5), 2x – 5y = –10 22. (1, 1), 3x + 2y = –7 23. (–6, –5), 4x + 3y = –6 24. (–3, 5), 5x – 6y = 9 25. GEOMETRY Quadrilateral ABCD has diagonals and . Determine whether is perpendicular to . Explain.
26. GEOMETRY Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6). Determine whether triangle ABC is a right triangle. Explain. 27. BUSINESS Brady’s Books is a retail store. The store’s average daily profits y are given by the equation y = 2x + 3 where x is the number of hours available for customer purchases. Brady’s adds an online shopping option. Write an equation in slope-intercept form to show a new profit line with the same profit rate containing the point (0, 12). 28. ARCHITECTURE The front view of a house is drawn on graph paper. The left side of the roof of the house is represented by the equation y = x. The rooflines intersect at a right angle and the peak of the roof is represented by the point (5, 5). Write the equation in slope-intercept form for the line that creates the right side of the roof. 29. ARCHAEOLOGY An archaeologist is comparing the location of a jeweled box she just found to the location of a brick wall. The wall can be represented by the equation y = x + 13. The box is located at the point (10, 9). Write an equation representing a line that is perpendicular to the wall and that passes through the location of the box. 30. GEOMETRY A parallelogram is created by the intersections of the lines x = 2, x = 6, y = x + 2, and another line. Find the equation of the fourth line needed to complete the parallelogram. The line should pass through (2, 0). (Hint: Sketch a graph to help you see the lines.) 31. INTERIOR DESIGN Pamela is planning to install an island in her kitchen. She draws the shape she likes by connecting the vertices of the square tiles on her kitchen floor. She records the location of each corner in the table.
Algebra 1 Section 5.3 Worksheet Justify each indicated step 1. t – 3 ≥ –15 2. 5(k + 8) – 7 ≤ 23 t – 3 + 3 ≥ –15 +3 a. ? 5k + 40 – 7 ≤ 23 a. ? t ≥ –12 5k + 33 ≤ 23 t ≥ (–12) b. ? 5k + 33 – 33 ≤ 23 – 33 b. ? t ≥ –16 5k ≤ –10
24. PLAYGROUND The perimeter of a rectangular playground must be no greater than 120 meters, because that is the total length of the materials available for the border. The width of the playground cannot exceed 22 meters. What are the possible lengths of the playground? 25. MEDICINE Clark’s Rule is a formula used to determine pediatric dosages of over-the-counter medicines. × adult dose = child dose a. If an adult dose of acetaminophen is 1000 milligrams and a child weighs no more than 90 pounds, what is the recommended child’s dose? b. This label appears on a child’s cold medicine. What is the adult minimum dosage in milliliters? Weight (lb) Age (yr) Dose under 48 under 6 call a doctor 48-95 6-11 2 tsp or 10 mL c. What is the maximum adult dosage in milliliters? 5-4 Practice Solving Compound Inequalities the solution set of each compound inequality. 1. –4 ≤ n ≤ 1 2. –4 ≤ p ≤ 4 3. x > 3 or x < 0 4. g < –3 or g ≥ 4 Write a compound inequality for each graph. 5. 6.