Writing Linear Equations
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- Camron Underwood
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1 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 = x y = x + 5y = 15 Write the slope-intercept form of the equation of the line through the given point with given slope. 4. through (1, 2); m = 7 5. through (3, 1); m = 1 6. through ( 2, 5); m = 4 Write the equation of a line in point-slope form through the given point. Then, express your final answer in slope-intercept form. = parallel, = perpendicular 2 7. (4, 2), to y = 2x (-3, 7) to y x 8 9. (-5, -1) to 2y 10 x 3 1
2 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. 1. y 3x y x 4 3. x = 4 AND y = 2 4. x 2y = 4 5. x + 3y = x 5y = 7 Length of a Segment Using Pythagorean Thm. Find the length of the segment (distance between each pair of points) with given endpoints using the Pythagorean Theorem, a b c 1. (0, 2) ; (4, 1) 2. (6, 7) ; (3, 5) 3. (5, 8) ; ( 8, 6) 2
3 Midpoint Formula For #1-3, use the Midpoint Formula to find the midpoint of the line segment with given endpoints. x1 x2 y1 y 2 Midpoint Formula M, (8, 9) ; (0, 5) 2. (1, 7) ; (6, 12) 3. (11, 8) ; ( 13, 3) Factoring Factor each polynomial below. These trinomials (3 terms) are in the form ax 2 + bx + c. These problems are factoring when a = 1. If an expression cannot be factored, write PRIME. 1. n 2 11n n 2 + 4n b b x 2 4x a a n 2 5n + 6 Geometry Vocabulary For the following geometry vocabulary terms, a definition is given. 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: Earth measurement (no sketch for this term) -the study of shapes and space 2. collinear: on the same line 3. coplanar: on the same plane 4. segment bisector: any segment, line, or plane that intersects a segment at its midpoint; i.e. cuts it in half 3
4 5. angle: 2 rays with a common endpoint called a vertex vertex: the common endpoint of an angle 6. right angle: an angle with a degree measure of 90 o 7. acute angle: an angle with a degree measure less than 90 o 8. obtuse angle: an angle with a degree measure between 90 o and 180 o 9. straight angle: an angle with a degree measure equal to 180 o 11. congruent: same shape and size; congruent segments have (no sketch for this term) the same length; congruent angles have equal measure 12. perpendicular lines: lines that intersect at right angles 13. complementary angles: two angles whose measure sums to 90 o 14. supplementary angles: two angles whose measure sums to 180 o 15. adjacent angles: angles that are next to each other; they must be in the same plane, share a vertex, share a side 16. linear pair: adjacent angles that are also supplementary 17. vertical angles: angles that are across from each other; they must not be adjacent and are formed from intersecting lines 18. polygon: closed figure made of line segments that do not intersect except at their endpoints 19. regular polygon: polygon with all sides congruent and all angles congruent Please fill in the table. A polygon with the following number of sides is called a... # Sides n Polygon Name 4
5 Geometry Introductory Problems Note: Knowledge of the above vocabulary terms is essential in completing the following problems. Refer to the figure to the right for # Name line TP, written as TP, in 2 different ways. sur suur 2. Name the plane that contains TN suur and QR in 2 different ways. 3. Name the intersection of lines g and h. 4. Name three collinear points. 5. Are points P, T, R, and M coplanar? Explain. 6. Name the angle from the model to the right in 3 different ways. The Segment-Addition Postulate states that a point B is between points A and C if and only if A, B, and C are collinear and AB + BC = AC. Basically, for a line segment, the sum of the parts of the segment = the whole length of the segment. 7. Use Segment Addition to solve for the variable. Point K is between J and L and JL is a line segment. (Hint: Draw a picture and then set up an equation!) a. JK = 6r, KL = r 2, and JL 27 b. JK 2 s, KL s 2, and JL 5s Find x. BD is a segment bisector. 5
6 Use the diagram to the right for #9-14. Name the vertex of each angle NMP Name the sides of each angle MOP Write another name for each angle. 13. QPR In the figure, CB uuur and CD uuur are opposite rays and CG uuur bisects FCB. 15. If m FCG = 2x + 19 and m GCB = 6x 9, find m GCB. 16. If m DCE = 2x + 10 and m ECB = 11x 12, find x. For the diagram at the right, name a pair of the following angles. 17. a. complementary angles b. supplementary angles c. adjacent angles d. linear pair e. vertical angles 18. BGD is a right angle. If m BGC = 16x - 4 and m CGD = 2x + 13, find x. 6
7 Answer Key ***You must show ALL work to receive credit for each problem in the summer assignment!!! ***Additionally, it is important to FIRST try the problem and then check your answer!!! ***Most answers are provided. Answers left blank will be graded for accuracy when submitted. Writing Linear Equations y = 4x 1 3. y = (-6/5)x y = -x y = -4x y = (3/2)x + (23/2) 9. y = 2x + 9 Graphing Lines Length of a Segment Using Pythagorean Thm Midpoint Formula 1. (4, -2) 2. (7/2, -19/2) 3. 7
8 Factoring 1. (n 10)(n 1) (b + 8)(b + 8) 4. prime (no two integers multiply to get 24 and add to get 4) 5. (a + 9)(a + 2) 6. (n 3)(n 2) Geometry Vocab -No Key. See online videos for assistance or note keys on my website. Geometry Introductory Problems suu r sr 1. (answers may vary) PT, g 2. (answers may vary) plane QTN 6. angle 4, angle A, angle BAC, angle CAB 7. a. r = 3 ; Note that r = -9 is a solution when you factor, but that would mean that JK = 6(-9) = -54 and you cannot have a negative length. That does not make sense. Therefore, r = -9 does not work. b. s = 6 8. x = M suuu r NM QPR, o a. COB and AOB d. EOD and DOB (answers may vary) 18. x = 4.5 (show work) 8
Writing Linear Equations
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 = 16 2. 13x 11y = 12 3. 4x y = 1
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