1. Home
  2. >Algebra
  3. >Linear Functions
Help

Parallel and perpendicular lines in linear functions

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
    • Definition of Parallel and Perpendicular Lines
    • How does that relate to slope?
?
Examples
Lessons
  1. Determine whether the three points A (-2,-1), B(0,4) & C(2,9) all lie on the same line.
    1. Determine the following slopes are parallel, perpendicular, or neither.
      i) m1=25,m2=25 m_1 = {2 \over 5}, m_2= {2 \over 5}

      ii) m1=15,m2=−51m_1 = {1 \over5} , m_2 = - {5 \over 1}

      iii) m1=47,m2=1221m_1 = {4 \over 7}, m_2 = {12 \over 21}

      iv) m1=m_1 = undefined, m2=0 m_2 = 0

      v) m1=mn−1;m2=−m−1bm_1 =mn^{-1}; m_2 =-m^{-1}b
      1. Given the points of two lines, determine when the lines are parallel, perpendicular or neither.
        1. Line 1: (3,2) & (1,4); Line 2: (-1,-2) & (-3,-4)
        2. Line 1: (5,6) & (7,8); Line 2: (-5,-6) & (-7,-8)
        3. Line 1: (0,4) & (-1,2); Line 2: (-3,5) & (1,7)
      2. Show that the points A(-3,0), B(1,2) and C(3,-2) are the vertices of a right triangle.
        1. Show that the points A(-1,-1), B(3,0), C(2,4) and D(-2,3) are the vertices of a square.
          Topic Notes
          ?
          Parallel lines are lines with identical slope. In other words, these lines will never cross each other. Perpendicular lines will always pass through each other and form right angles at the interception. In this lesson, we will learn how to use information such as, points in lines and their slopes, to determine whether the lines are parallel, perpendicular or neither.
          Parallel
          lines          − - identical slope so they never intersect each other, unless overlapped.

          Perpendicular
          lines          − - two lines form right angles to each other when they intersect. If the slope of first line is ab {a \over b} , the slope of perpendicular line is the slope of perpendicular line is −ba - {b \over a} . The product of the two slopes is -1.
          Basic Concepts
          ?
          Related Concepts
          ?