Writing Linear Equations
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- Curtis Griffin
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1 Writing Linear Equations Name: SHOW ALL WORK!!!!! For full credit, show all work on all problems! Write the slope-intercept form of the equation of each line. 1. 3x 2y = x 11y = x y = x + 5y = 15 Write the slope-intercept form of the equation of the line through the given point with given slope. 5. through (1, 2); m = 7 6. through (3, 1); m = 1 7. through ( 2, 5); m = 4 8. through (3, 5); m = 3 5 Write the equation of a line in point-slope form with the given conditions. Then, express your final answer in slope-intercept form. = parallel, = perpendicular 9. through (4, 2), to y = 2x through (-3, 7) to 2 y = x
2 11. through (0, -4) to 9 y = x through (-5, -1) to 2y 10 = x 7 Graphing Lines Graph each line using the slope-intercept method. If the equation is not in slope-intercept form, first put it in that form and then graph the line using the slope and y-intercept y = 3x 5 2. y = x 3. x = 4 AND y = x 2y = 4 5. x + 3y = x 5y = 7 2
3 Distance Formula Find the distance between each pair of points using the distance formula or Pythagorean Theorem. Distance Formula d = ( x x ) + ( y y ) ; Pythagorean Theorem: (0, 2) ; (4, 1) 2. (6, 7) ; (3, 5) a + b = c 3. (5, 8) ; ( 8, 6) 4. (7, 3) ; ( 1, 4) 5. ( 7, 0) ; ( 2, 4) 6. (15, 3) ; ( 6, 9) Midpoint Formula Use the Midpoint Formula to find the midpoint of the line segment with the given endpoints. Midpoint Formula d = ( x x ) + ( y y ) (8, 9) ; (0, 5) 2. ( 4, 2) ; (2, 3) 3. (1, 7) ; (6, 12) 4. (11, 8) ; ( 13, 3) 3
4 Given the midpoint and one endpoint of a line segment, find the other endpoint. 5. Endpoint: (10, 12) 6. Endpoint: (-11, 9) 7. Endpoint: (7, 4) Midpoint (6, 9) Midpoint (3, -11) Midpoint (8, 2 3 ) Factoring Factor each expression. These trinomials (3 terms) are in the form ax 2 + bx + c. Factoring Trinomials (a = 1) Factoring Trinomials (a > 1) 1. n 2 11n p 2 2p 5 2. n 2 + 4n b b x 2 4x a a n 2 8n v v n 2 5n a a n n a 2 a z 2 27z v 2 30v k 2 4k n 2 15n y 2 17y + 4 4
5 Solving Equations Solve each equation. Some equations will require factoring (t + 2) = 4 (3 + t) 2. 8x 2 = x + 1 = (4k + 5)(k + 1) = 0 5. x 2 11x + 24 = n 2 18n 18 = r 2 16r 7 = x = 59x 9. 3 x 2 = 4( x + 7) = x + 2 5x x = 1 x Solve for y: 3y + z = am 4y 13. Solve for x: 3ax n = 4 5 5
6 Simplifying Radicals 3 2 Examples 25 = 5 ; 50 = 25 2 = 5 2 ; 18x = 9 2 x x = 3 2 x x = 3x 2x *Another strategy is to make a factor tree!!! Simplify each radical expression: *Leave your answers in simplest radical form!!! (No decimals!) c x 5 3x ( 15 60) Simplify each expression by FOIL. FOIL 1. (x + 4)(x 9) 2. (2z 1)(z + 7) 3. (5b + 4) 2 4. ( 2 6) 2 6
7 Geometry Vocabulary Define each of the following geometry vocabulary terms and then draw a sketch illustrating each term. Feel free to look up each term online or in my online notes from my website!!! Definition Sketch/Illustration/Example 1. geometry (no sketch) 2. point, line, & plane *Be able to name points, lines & planes!!! (2 points for a line, 3 non-collinear points for a plane) 3. collinear 4. coplanar 5. line 6. line segment 7. segment bisector 8. ray 9. angle 10. sides of an angle 7
8 11. vertex 12. right angle 13. acute angle 14. obtuse angle 15. straight angle Ways to Name an angle 17. Congruent 18. perpendicular lines 19. complementary angles 20. supplementary angles 21. adjacent angles 22. linear pair 23. vertical angles 24. polygon 8
9 Please fill in the table. A polygon with the following number of sides is called a... # Sides n Polygon Name 25. convex polygon 26. concave polygon 27. regular polygon 28. parallel ( ) lines 29. slopes of lines vs. slopes of lines 30. parallel planes 31. skew lines 32. transversal 33. corresponding angles 34. same-side interior angles (consecutive interior angles) 9
10 35. alternate interior angles 36. alternate exterior angles Geometry Introductory Problems Answer each question below. Note: Knowledge of the above vocabulary terms will be essential in completing the following problems. Again, please use the Internet and my website for guidance!!! Refer to the figure for # Name a line that contains points T and P in 2 different ways. 2. Name the plane that contains TN and QR in 2 different ways. 3. Name a line that contains points T and M in 2 different ways. Refer to the figure for # How many planes are shown in the figure? 5. Name three collinear points. 6. Are points N, R, S, and W coplanar? Explain. 7. The Segment-Addition Postulate states that a point M is between points P and Q if and only if P, Q, and M are collinear and PM + MQ = PG. Basically, for a line segment, the sum of the parts of the segment = the whole length of the segment. Use Segment Addition to solve for the variable. a. JK = 6r, KL = r 2, and JL = 27 b. JK = 2 s, KL = s + 2, and JL = 5s 10 10
11 8. Find x. Assume BD is a segment bisector. Name the vertex of each angle NMP Name the sides of each angle MOP Write another name for each angle. 13. QPR Classify each angle as right, acute, obtuse, or straight. 15. UZW 16. YZU 17. TZY 18. UZT In the figure, CB and CD are opposite rays, CE bisects DCF, and CG bisects FCB. 19. If m FCG = 24 and m GCB = 13x - 11, find m GCB. 20. If m DCE = 12 x and m ECF = , find m DCE. 9 11
12 Name a pair of the following angles. 21. a. complementary angles b. supplementary angles c. adjacent angles d. linear pair e. vertical angles f. adjacent angles 22. BGD is a right angle. If m BGC = 16x - 4 and m CGD = 2x + 13, find x. 23. Name each polygon and then classify it as convex or concave and regular or irregular. a. b. c. 24. Name all planes that are parallel to plane DHE. 25. Name all segments that are parallel to AB. 26. Name all segments that are skew to CD. 27. Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles, linear pair, or vertical. a. 2 and 8 d. 3 and 6 b. 8 and 5 e. 12 and 10 c. 1 and 9 f. 3 and 9 12
Writing Linear Equations
Complete ALL problems. Show your work. Check your answers on the back page! Writing Linear Equations Write the slope-intercept form of the equation of each line. 1. 3x 2y = 16 2. 4x y = 1 3. 6x + 5y =
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