Graphing Linear Equations and Inequalities

Name: Date: Pd. Graphing Linear Equations and Inequalities Unit 2 Review 1. Concepts and Vocabulary 1. What are the 3 methods we have learned to graph equations? 2. Which equation would produce a VERTICAL line when graphed: x = 2 or y = 27 3. Which equation would produce a HORIZONTAL line when graphed: x = 2 or y =2? 4. If a line has a ZERO slope, is it horizontal or vertical? 5. If a line has an UNDEFINED slope, is it horizontal or vertical? 6. Simplify: a. 0/10 = 67 10 b.7 7. If = - 3/4 are both the 3 and the 4 negative? 8. Write two different formulas we use to find slope. 9. Give the coordinates AND the quadrant for each point. A (3,3) B(-2,4) c(0,-4) 4 + - a * x / 5 D (5,0) X-axis B la. Ordered Pairs b. SIF c. Intercepts 2. X = 2 3. 4. horizontal 5. Vertical A 2 C II. Use a table of values to graph each equation (HINT: Get y alone first!) 10. x + 2y = - 2 y_{1} = - 1/2 * x - 1 X Y Work - 1/2 * (2) - 1 0-1 - 1/2 * (- 2) - 1 11. y = 4 24 X Y Work -24 0 4 44 y = 2 ба. 0 b. Undefined 7. No 8. a. rise run b. (y_{1} - y_{1})/(x_{1} - x_{1}) 9. 10. See left. 11. See left. Algebra 1a 654-3-2-10 1134 R.Unit 2 (2y)/4 = (- x - 2)/z Name: Date: Pd. III. Write each equation in slope-intercept form. Identify the slope and y-intercept. 12. aligned 6x-12y=24\\ - x aligned y = 1/2 * x - 2 (- 12y)/- 12 = (- 6x + 24)/- 12 13. (- 4y)/- 4 = (2x)/- 4 y = - 1/2 * x m = - 1/2 k = 0 14. - 4x - 3y = 9 + x 4f = - 5/3 * (- 3) (- 3y)/- 3 = (5x + 9)/- 3 4x IV. Graph by using the x- and y-intercepts. Show ALL work. (Hint: Plug in zeros!) 15 x - inL = (2, 0) 15. - 2y = - 4x + 8 4x - 2y / d = 8 4x = 8 x = 0 (2,0) (0) - x - 4y = - 4 X ^ *W ( 4g ) (x - v + (y + z))/(- z * z = - z * y) y = 1 y - i * nt .= underline (0 2 -4) x-int.= (4, 0) y - inL = (0, 1) 17 - 13/21 18. 0 V. Determine the slope of the line that passes through each pair of points. 17. (17,3 (- 4, 10) x + 4 m = (10 - (- 3))/(- 4 - 17) = 13/- 21 VI. Reading Graphs 20. Based on the graph to the right: Give 3 solutions (ordered pairs) to the equation. (4-2) (-3,5) (-2,4) Also identify, x-intercept, y-intercept and slope. y -int=2 x -int=2 -2 VII. Graph each equation using slope-intercept form (identify m & b firstl). 21. y = - 3/4 * x + 4 b = 4 Algebra 10 22. x + y = - 2 y = - x - 2 b = - 2 m / (- l) 19. 7/8 18. and ( 2 ^ 2 - 100 ^ 2 (0, - 100) m = (- 100 - (- 100))/(2 + 0) - 0/2 = 0 19. (3,9) and (19,5) m = (5 - (- 9))/(19 - 3) = 14/16 = 7/8 20. a. (4,-2) -6-5-4-3-2-10 123456 b. (-3,5) c. (-2,4) x - int = c ^ 7 y - int = 0 22. b = 4 b = - 2 R. Unit 2 m = - 3/4 m = 2/- 2 = - 1 m = (u_{1} - y_{1})/(x_{2} - x_{1}) m = - l m=\ - 5/3 m = - 3/4 m = - 1/2 b =\ 2 y = - 4 - 4y = - 4 m = 1/2 b = - 3 - 2y = 8 m = 1/2 * b = - 2 b = Q Name: Date: Pd. 4 23. 2x - 3y = 6 -24 (- 8y)/- 3 = (- 2x + 6)/- 3 y = 2/3 * x - 2 m = 2/5 b = - 2 24. - x - 3y = 3 + x + x (- 3y)/- 3 = (x + 3)/- 3 (LJ)/G =- 1 D forall J=1 b = - 1 23 m = - 2/5 b = - 2 24 m = - 1/3 b = - 1 25. Multiple Choice. Which equation is shown here? meg slope b = 2 x = - 3 25. F a) y = 3x + 2 b) y = - 3x + 2 c) y = 3x - 2 26. See left. d) y = - 3x - 2 e) y = 1/3 * x - 2 y = - 1/3 * x + 2 27. See left. 28. See left. 29. See left. VIII. Graph the following inequalities. 26. y < 2/3 * x + 2 m = 2/5 b = 2 Dashed Shode underline (heck (0, e) 0 < 2 27. 3x - 9y < 27 (- 9y)/- 9 < (- 3x + 27)/- 9 1y > 1/8 * x - 3 m+1 m = 1/3 b = - 3 Shade Check (0,0) 0-6427 0427 2 28. x - y <= 2 (- y)/- 1 <= (x + 2)/- 1 y >= x - 2 m = 1 b = - 2 Solid Shade ↑ Chierk (0,0) 0 <= 2 0 <= 2 29. (- 3y)/- 3 >= 6/- 3 y <= - 2 m = 0 b = - 2 Solid Shade 123456 Hoy