This line is called the perpendicular bisector. 0 = 2 + c Is your friend correct? x = 35 and y = 145, Question 6. x = 6 Question 22. Answer: Hence, from the above, We know that, EG = \(\sqrt{50}\) We know that, A(3, 4),y = x + 8 We can conclude that the parallel lines are: If you will see a tiger, then you go to the zoo-> False. We want to prove L1 and L2 are parallel and we will prove this by using Proof of Contradiction 2x + y + 18 = 180 In Exercises 13 16. write an equation of the line passing through point P that s parallel to the given line. Possible answer: plane FJH 26. plane BCD 2a. According to Corresponding Angles Theorem, Hence, Likewise, parallel lines become perpendicular when one line is rotated 90. Answer: Another answer is the line perpendicular to it, and also passing through the same point. y = \(\frac{1}{2}\)x + 1 -(1) Name a pair of perpendicular lines. y = 4x 7 Question 22. A(3, 4), y = x = (-1, -1) Make a conjecture about what the solution(s) can tell you about whether the lines intersect. Answer: If parallel lines are cut by a transversal line, thenconsecutive exterior anglesare supplementary. From Example 1, 2x y = 4 If twolinesintersect to form a linear pair of congruent angles, then thelinesareperpendicular. The points are: (0, 5), and (2, 4) Answer: The equation of a line is: Use these steps to prove the Transitive Property of Parallel Lines Theorem Possible answer: plane FJH plane BCD 2a. a. 2 and 3 Point A is perpendicular to Point C Hence, from the above figure, Substitute (0, 1) in the above equation y = 3x + 9 -(1) Hence, from the above, 10) Slope of Line 1 12 11 . d = \(\sqrt{(x2 x1) + (y2 y1)}\) Hence, The equation that is parallel to the given equation is: From the given figure, XY = \(\sqrt{(3 + 3) + (3 1)}\) In Exercises 11-14, identify all pairs of angles of the given type. 8 = -2 (-3) + b We know that, 4 5, b. The given point is: A (-6, 5) c = -1 A(2, 0), y = 3x 5 The given lines are: The sum of the angle measure between 2 consecutive interior angles is: 180 We can observe that when r || s, From the figure, Solving Equations Involving Parallel and Perpendicular Lines www.BeaconLC.org2001 September 22, 2001 9 Solving Equations Involving Parallel and Perpendicular Lines Worksheet Key Find the slope of a line that is parallel and the slope of a line that is perpendicular to each line whose equation is given. \(\frac{6 (-4)}{8 3}\) We know that, If the slopes of two distinct nonvertical lines are equal, the lines are parallel. A (x1, y1), B (x2, y2) We can say that any parallel line do not intersect at any point So, So, From the given figure, We can observe that Answer: These Parallel and Perpendicular Lines Worksheets will show a graph of a series of parallel, perpendicular, and intersecting lines and ask a series of questions about the graph. To find the value of c, 5 = \(\frac{1}{3}\) + c Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y. Answer: Question 38. Hence, from the above, The opposite sides are parallel and the intersecting lines are perpendicular. answer choices Parallel Perpendicular Neither Tags: MGSE9-12.G.GPE.5 Question 7 300 seconds A(8, 0), B(3, 2); 1 to 4 The equation for another perpendicular line is: Question 12. x = \(\frac{4}{5}\) Determine the slopes of parallel and perpendicular lines. With Cuemath, you will learn visually and be surprised by the outcomes. Algebra 1 Parallel and Perpendicular lines What is the equation of the line written in slope-intercept form that passes through the point (-2, 3) and is parallel to the line y = 3x + 5? 1 8, d. m6 + m ________ = 180 by the Consecutive Interior Angles Theorem (Thm. Determine the slope of parallel lines and perpendicular lines. y = -3 (0) 2 Now, Answer: Since it must pass through \((3, 2)\), we conclude that \(x=3\) is the equation. Substitute A (3, -1) in the above equation to find the value of c We know that, We can conclude that \(\overline{K L}\), \(\overline{L M}\), and \(\overline{L S}\), d. Should you have named all the lines on the cube in parts (a)-(c) except \(\overline{N Q}\)? We can observe that there is no intersection between any bars The points are: (3, 4), (\(\frac{3}{2}\), \(\frac{3}{2}\)) Answer: (2x + 20) = 3x Draw an arc by using a compass with above half of the length of AB by taking the center at A above AB So, We can say that any coincident line do not intersect at any point or intersect at 1 point We can conclude that quadrilateral JKLM is a square. Hence, from the above, Parallel to \(x+y=4\) and passing through \((9, 7)\). Justify your answer for cacti angle measure. corresponding We can observe that x and 35 are the corresponding angles A(- 6, 5), y = \(\frac{1}{2}\)x 7 Corresponding Angles Theorem Copy and complete the following paragraph proof of the Alternate Interior Angles Converse using the diagram in Example 2. To find the coordinates of P, add slope to AP and PB The given figure is: m2 = -1 Two lines, a and b, are perpendicular to line c. Line d is parallel to line c. The distance between lines a and b is x meters. Answer: Question 36. When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the Consecutive interior angles The slope of the parallel equations are the same = \(\frac{-3}{4}\) Substitute A (2, -1) in the above equation to find the value of c (1) = Eq. It is given that the given angles are the alternate exterior angles We can conclude that the plane parallel to plane LMQ is: Plane JKL, Question 5. Write the equation of the line that is perpendicular to the graph of 6 2 1 y = x + , and whose y-intercept is (0, -2). Answer: In Exercises 9 and 10, use a compass and straightedge to construct a line through point P that is parallel to line m. Question 10. Name a pair of parallel lines. The given point is: (-3, 8) Compare the given coordinates with d = \(\sqrt{(x2 x1) + (y2 y1)}\) Hence, ANALYZING RELATIONSHIPS = \(\frac{10}{5}\) Parallel and Perpendicular Lines Maintaining Mathematical Proficiency Find the slope of the line. y = \(\frac{1}{2}\)x + c The coordinates of the meeting point are: (150, 200) In Example 4, the given theorem is Alternate interior angle theorem By using the linear pair theorem, So, Answer: Answer: Answer: (a) parallel to the line y = 3x 5 and From the given figure, To find the value of b, Answer: If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line So, Question 5. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem. 3.4). (x1, y1), (x2, y2) XY = \(\sqrt{(x2 x1) + (y2 y1)}\) x = 90 We know that, We can conclude that We can conclude that the number of points of intersection of intersecting lines is: 1, c. The points of intersection of coincident lines: A(15, 21), 5x + 2y = 4 The parallel line needs to have the same slope of 2. = \(\frac{1}{-4}\) The given point is: C (5, 0) Now, The coordinates of the line of the second equation are: (-4, 0), and (0, 2) So, So, P = (4 + (4 / 5) 7, 1 + (4 / 5) 1) y = 3x 5 Answer: The equation that is parallel to the given equation is: We can conclude that 1 = 60. So, We can observe that the given lines are perpendicular lines b = -5 b = 19 Chapter 3 Parallel and Perpendicular Lines Key. Explain your reasoning. Difference Between Parallel and Perpendicular Lines, Equations of Parallel and Perpendicular Lines, Parallel and Perpendicular Lines Worksheets. The given figure is: In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y. AP : PB = 3 : 2 We can say that w and v are parallel lines by Perpendicular Transversal Theorem We can conclude that : n; same-side int. m1m2 = -1 We can say that w and x are parallel lines by Perpendicular Transversal theorem. The slope of the equation that is parallel t the given equation is: \(\frac{1}{3}\) 3.2). y = -2x 1 (2) From Exploration 2, We can conclude that Answer: According to the Converse of the Corresponding angles Theorem, Explain your reasoning. Hence, from the above, If you multiply theslopesof twoperpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals. Explain your reasoning. We know that, Parallel lines do not intersect each other From the given figure, 1 = 60 y = 3x 6, Question 20. The equation of the line that is parallel to the given line equation is: 1 = 3 (By using the Corresponding angles theorem) Find the equation of the line perpendicular to \(x3y=9\) and passing through \((\frac{1}{2}, 2)\). Hence, from the above, We know that, d = | 2x + y | / \(\sqrt{5}\)} Now, Hence, from the above, Answer: Proof: From the given figure, We know that, Answer: We know that, We know that, Similarly, observe the intersecting lines in the letters L and T that have perpendicular lines in them. From the given figure, = 1 Slope of MJ = \(\frac{0 0}{n 0}\) Example 2: State true or false using the properties of parallel and perpendicular lines. From the above figure, So, x = 4 Now, x and 97 are the corresponding angles Write an equation of a line perpendicular to y = 7x +1 through (-4, 0) Q. So, Hence, from the above figure, In Euclidean geometry, the two perpendicular lines form 4 right angles whereas, In spherical geometry, the two perpendicular lines form 8 right angles according to the Parallel lines Postulate in spherical geometry. The slope of the parallel line is 0 and the slope of the perpendicular line is undefined. transv. The given point is: A (8, 2) So, Some examples follow. So, m1 = \(\frac{1}{2}\), b1 = 1 So, Explain your reasoning. So, Answer: Compare the given coordinates with Hence, The plane parallel to plane ADE is: Plane GCB. c = 0 Justify your conjecture. Find the value of x that makes p || q. (E) We know that, The slope of line a (m) = \(\frac{y2 y1}{x2 x1}\) We can observe that 3 and 8 are consecutive exterior angles. ERROR ANALYSIS To find the value of c, -2 = 3 (1) + c The given figure is: The given figure is: Write an equation of the line that passes through the given point and has the given slope. Answer: We know that, Consecutive Interior Angles Theorem (Thm. 8 = \(\frac{1}{5}\) (3) + c Answer: So, The points are: (-2, 3), (\(\frac{4}{5}\), \(\frac{13}{5}\)) If the slope of one is the negative reciprocal of the other, then they are perpendicular. We can observe that when p || q, (13, 1) and (9, 4) Explain our reasoning. What does it mean when two lines are parallel, intersecting, coincident, or skew? 3 + 8 = 180 We can observe that The equation of the line that is parallel to the given line equation is: For parallel lines, Question 15. We can conclude that According to the Alternate Interior Angles Theorem, the alternate interior angles are congruent MAKING AN ARGUMENT We know that, According to the consecutive Interior Angles Theorem, We can conclude that the alternate exterior angles are: 1 and 8; 7 and 2. From the given coordinate plane, Click here for a Detailed Description of all the Parallel and Perpendicular Lines Worksheets. \(\frac{1}{2}\)x + 7 = -2x + \(\frac{9}{2}\) x = \(\frac{69}{3}\) Hence, from the above, (C) Answer: From the given figure, You and your mom visit the shopping mall while your dad and your sister visit the aquarium. Now, Solution: Using the properties of parallel and perpendicular lines, we can answer the given . The vertical angles are: 1 and 3; 2 and 4 The slope of PQ = \(\frac{y2 y1}{x2 x1}\) Perpendicular lines are denoted by the symbol . = 2 x = 60 Write an equation of the line that is (a) parallel and (b) perpendicular to the line y = 3x + 2 and passes through the point (1, -2). x + x = -12 + 6 The representation of the complete figure is: PROVING A THEOREM (- 1, 5); m = 4 The given coplanar lines are: We can conclude that the distance from point A to the given line is: 8.48. Line 2: (7, 0), (3, 6) Answer: Now, The line l is also perpendicular to the line j Question 3. 12. From the given figure, We know that, c. y = 5x + 6 alternate interior Begin your preparation right away and clear the exams with utmost confidence. The given equation is: 20 = 3x 2x Which theorems allow you to conclude that m || n? The given equation is: Explain. We can conclude that the value of x is: 60, Question 6. From the given figure, We know that, d = \(\sqrt{(x2 x1) + (y2 y1)}\) Answer: = 6.26 Angles Theorem (Theorem 3.3) alike? line(s) parallel to X (-3, 3), Y (3, 1) BCG and __________ are consecutive interior angles. A (-2, 2), and B (-3, -1) When you look at perpendicular lines they have a slope that are negative reciprocals of each other. Perpendicular lines do not have the same slope. Now, Is it possible for consecutive interior angles to be congruent? Answer: Now, 0 = \(\frac{1}{2}\) (4) + c So, The vertical angles are congruent i.e., the angle measures of the vertical angles are equal The slope of vertical line (m) = \(\frac{y2 y1}{x2 x1}\) For example, the opposite sides of a square and a rectangle have parallel lines in them, and the adjacent lines in the same shapes are perpendicular lines. Section 6.3 Equations in Parallel/Perpendicular Form. Hence, from the above, y = \(\frac{1}{3}\)x 2. Construct a square of side length AB We can observe that, The given point is: P (4, -6) Write the Given and Prove statements. The "Parallel and Perpendicular Lines Worksheet (+Answer Key)" can help you learn about the different properties and theorems of parallel and perpendicular lines. So, Hence, from the above, Explain why the tallest bar is parallel to the shortest bar. (5y 21) ad (6x + 32) are the alternate interior angles The given figure is: -9 = \(\frac{1}{3}\) (-1) + c Alternate Exterior Angles Converse (Theorem 3.7) c = 6 0 Hence, from the above, The representation of the Converse of the Consecutive Interior angles Theorem is: Question 2. The lines that do not intersect and are not parallel and are not coplanar are Skew lines Hence, from the above, Question 1. When two lines are cut by a transversal, the pair ofangles on one side of the transversal and inside the two lines are called the Consecutive interior angles Hence, d = | 2x + y | / \(\sqrt{2 + (1)}\) Substitute A (3, -4) in the above equation to find the value of c EG = 7.07 In Exploration 1, explain how you would prove any of the theorems that you found to be true. To find the value of c, Answer: We know that, A (x1, y1), and B (x2, y2) Hence, from the above, Perpendicular lines have slopes that are opposite reciprocals. Justify your conjecture. We can say that (a) parallel to and a. Prove: AB || CD By comparing the given pair of lines with c = 2 To find the distance from point X to \(\overline{W Z}\), Parallel and Perpendicular Lines From the given slopes of the lines, identify whether the two lines are parallel, perpendicular, or neither. Answer: Lines Perpendicular to a Transversal Theorem (Theorem 3.12): In a plane. In Exercise 31 on page 161, a classmate tells you that our answer is incorrect because you should have divided the segment into four congruent pieces. So, Now, Hence, from the above, = 2, The slope of line b (m) = \(\frac{y2 y1}{x2 x1}\) Now, The product of the slopes of perpendicular lines is equal to -1 m = -1 [ Since we know that m1m2 = -1] and N(4, 1), Is the triangle a right triangle? 4 = 2 (3) + c Slope of line 2 = \(\frac{4 + 1}{8 2}\) From the given figure, 1 = 123 and 2 = 57. Question 35. y = 3x 6, Question 11. Parallel to \(10x\frac{5}{7}y=12\) and passing through \((1, \frac{1}{2})\). Determine whether quadrilateral JKLM is a square. So, AO = OB To find the y-intercept of the equation that is perpendicular to the given equation, substitute the given point and find the value of c, Question 4. Hence, We can conclude that c = -2 Now, So, So, m1m2 = -1 (B) intersect Lines l and m are parallel. When we observe the Converse of the Corresponding Angles Theorem we obtained and the actual definition, both are the same We can conclude that the given pair of lines are parallel lines. y = \(\frac{1}{7}\)x + 4 Hw Key Hw Part 2 key Updated 9/29/22 #15 - Perpendicular slope 3.6 (2017) #16 - Def'n of parallel 3.1 . c = 3 The points of intersection of intersecting lines: the equation that is perpendicular to the given line equation is: The slope of the perpendicular line that passes through (1, 5) is: 2x = 120 The given point is: A (2, 0) No, p ||q and r ||s will not be possible at the same time because when p || q, r, and s can act as transversal and when r || s, p, and q can act as transversal. m1 m2 = -1 P = (3.9, 7.6) Check out the following pages related to parallel and perpendicular lines. Parallel to \(\frac{1}{5}x\frac{1}{3}y=2\) and passing through \((15, 6)\). We have to find the point of intersection In Exploration 2. m1 = 80. We can conclude that Given m1 = 115, m2 = 65 For example, PQ RS means line PQ is perpendicular to line RS. b = 9 Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). By using the Perpendicular transversal theorem, Hence, from the above, CONSTRUCTING VIABLE ARGUMENTS These worksheets will produce 6 problems per page. We can conclude that the vertical angles are: The given figure is: Hence, from the above, The coordinates of line b are: (3, -2), and (-3, 0) Alternate Interior angles are a pair of angleson the inner side of each of those two lines but on opposite sides of the transversal. Your school has a $1,50,000 budget. Hence, from the above, In other words, If \(m=\frac{a}{b}\), then \(m_{\perp}=-\frac{b}{a}\), Determining the slope of a perpendicular line can be performed mentally. So, The point of intersection = (\(\frac{4}{5}\), \(\frac{13}{5}\)) 1 = 2 = 3 = 4 = 5 = 6 = 7 = 8 = 80, Question 1. c = 4 3 To find the coordinates of P, add slope to AP and PB Hence, Now, a.) The given figure is: The Intersecting lines are the lines that intersect with each other and in the same plane P = (2 + (2 / 8) 8, 6 + (2 / 8) (-6)) According to this Postulate, Hence, from the above figure, CONSTRUCTION c.) Parallel lines intersect each other at 90. Parallel lines are two lines that are always the same exact distance apart and never touch each other. c = \(\frac{40}{3}\) Explain your reasoning. Answer: Hence, from the above, 4 5 and \(\overline{S E}\) bisects RSF. Parallel to \(y=\frac{1}{2}x+2\) and passing through \((6, 1)\). 1 = 180 140 The two lines are Skew when they do not intersect each other and are not coplanar, Question 5. These worksheets will produce 6 problems per page. Line 2: (2, 1), (8, 4) We know that, So, c = -4 + 3 2 = 180 47 Classify each pair of angles whose measurements are given. Given Slope of a Line Find Slopes for Parallel and Perpendicular Lines Worksheets We can conclude that it is not possible that a transversal intersects two parallel lines. m2 = -1 Hence, y = \(\frac{1}{2}\)x + 2 y = 7 Given m3 = 68 and m8 = (2x + 4), what is the value of x? We can conclude that the theorem student trying to use is the Perpendicular Transversal Theorem. 2 = 57 The coordinates of the meeting point are: (150. \(\frac{13-4}{2-(-1)}\) \(\overline{A B}\) and \(\overline{G H}\), b. a pair of perpendicular lines (-1) (m2) = -1 In Exercises 15-18, classify the angle pair as corresponding. The coordinates of line a are: (0, 2), and (-2, -2) WRITING So, You meet at the halfway point between your houses first and then walk to school. Label the intersection as Z. Hence, from the above, 1 = 40 Answer: Question 34. b. m1 + m4 = 180 // Linear pair of angles are supplementary 1 = 41 We can conclude that, -4 = \(\frac{1}{2}\) (2) + b Now, m = \(\frac{1}{4}\) 2x and 2y are the alternate exterior angles The line x = 4 is a vertical line that has the right angle i.e., 90 Now, = \(\frac{8}{8}\) The lines skew to \(\overline{Q R}\) are: \(\overline{J N}\), \(\overline{J K}\), \(\overline{K L}\), and \(\overline{L M}\), Question 4. a. Compare the given equation with b. To find the value of c in the above equation, substitue (0, 5) in the above equation 2 = \(\frac{1}{4}\) (8) + c We can conclude that the distance that the two of the friends walk together is: 255 yards. x = 12 and y = 7, Question 3. In the same way, when we observe the floor from any step, Answer: Question 2. Which of the following is true when are skew? Slope (m) = \(\frac{y2 y1}{x2 x1}\) Answer: x + 2y = 2 Write an equation of a line parallel to y = x + 3 through (5, 3) Q. From the given figure, \(\frac{5}{2}\)x = 2 Solving the concepts from the Big Ideas Math Book Geometry Ch 3 Parallel and Perpendicular Lines Answers on a regular basis boosts the problem-solving ability in you. a. a pair of skew lines Explain your reasoning. d = | ax + by + c| /\(\sqrt{a + b}\) Use the diagram. If the corresponding angles are congruent, then the two lines that cut by a transversal are parallel lines The given expression is: A bike path is being constructed perpendicular to Washington Boulevard through point P(2, 2). 8x = (4x + 24) x = 4 Now, We know that, (1) ATTENDING TO PRECISION So, 0 = \(\frac{1}{2}\) (4) + c x = 20 m1 m2 = \(\frac{1}{2}\) c = 5 Hence, Answer: Hence, from the above, y = \(\frac{1}{4}\)x + b (1) Does either argument use correct reasoning? (1) From the above diagram, Justify your answer. We know that, EG = \(\sqrt{(5) + (5)}\) Identify all the linear pairs of angles. x = 12 Negative reciprocal means, if m1 and m2 are negative reciprocals of each other, their product will be -1. Question 37. We can conclude that the argument of your friend that the answer is incorrect is not correct, Think of each segment in the figure as part of a line. Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are parallel if their slopes are the same, \(m_{1}=m_{2}\). We can conclude that the value of XZ is: 7.07, Find the length of \(\overline{X Y}\) Hence, Answer: 1 = 2 = 42, Question 10. Let's expand 2 (x 5) and then rearrange: y 4 = 2x 10. The following table shows the difference between parallel and perpendicular lines. y = -x 12 (2) Compare the given equation with Now, To find the coordinates of P, add slope to AP and PB We get 3.4) Question 21. PROVING A THEOREM Hence, from the above, The given equation is: Hence, Therefore, they are perpendicular lines. \(m_{}=10\) and \(m_{}=\frac{1}{10}\), Exercise \(\PageIndex{4}\) Parallel and Perpendicular Lines. The given figure is: The equation that is perpendicular to the given line equation is: The given figure is: The 2 pair of skew lines are: q and p; l and m, d. Prove that 1 2. Hence, XZ = \(\sqrt{(4 + 3) + (3 4)}\) y = 2x + c2, b. The line y = 4 is a horizontal line that have the straight angle i.e., 0 (- 8, 5); m = \(\frac{1}{4}\) = 8.48 2x + y = 180 18 The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular line Seeking help regarding the concepts of Big Ideas Geometry Answer Key Ch 3 Parallel and Perpendicular Lines? AB = 4 units What is the relationship between the slopes? Answer: We can observe that The given figure is: The letter A has a set of perpendicular lines. We know that, 11y = 96 19 y = \(\frac{2}{3}\)x + 1, c. Possible answer: 2 and 7 c. Possible answer: 1 and 8 d. Possible answer: 2 and 3 3. Answer: Slope of ST = \(\frac{1}{2}\), Slope of TQ = \(\frac{3 6}{1 2}\) 3 + 4 + 5 = 180 The length of the field = | 20 340 | Hence, from the above figure, \(\frac{1}{2}\)x + 1 = -2x 1 What are Parallel and Perpendicular Lines? FCA and __________ are alternate exterior angles. (7x 11) = (4x + 58) (1) with the y = mx + c, So, 1 3, We can conclude that the given lines are neither parallel nor perpendicular. To be proficient in math, you need to analyze relationships mathematically to draw conclusions. Question 42. In Exercises 3 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. In Exercises 3 and 4. find the distance from point A to . The given equation is: Parallel lines are those that never intersect and are always the same distance apart. b is the y-intercept We can conclude that the value of XY is: 6.32, Find the distance from line l to point X. x = 14 REASONING We can conclude that a line equation that is perpendicular to the given line equation is: Hence, From the given figure, (D) A, B, and C are noncollinear. From the given figure, x = 107 Using P as the center, draw two arcs intersecting with line m. The product of the slopes of the perpendicular lines is equal to -1 From the given figure, So, We can conclude that FCA and JCB are alternate exterior angles. Question 25. a.) Example: Write an equation in slope-intercept form for the line that passes through (-4, 2) and is perpendicular to the graph of 2x - 3y = 9. Hence, from the above, Explain. Write the equation of the line that is perpendicular to the graph of 53x y = , and 10x + 2y = 12 PROOF (b) perpendicular to the given line. Answer: From the given coordinate plane, Let the given points are: A (-1, 2), and B (3, -1) Compare the given points with A (x1, y1), B (x2, y2) We know that, Slope of the line (m) = \frac {y2 - y1} {x2 - x1} So,
