Question
upstudy study bank question image url

Lines Identifying parallel and perpendicular lines from equations The equations of three lines are given below. Line 1: \( 4 x+6 y=-4 \) Line 2: \( 2 y=-3 x+5 \) Line \( 3: y=-\frac{3}{2} x+8 \) For each pair of lines, determine whether they are parallel, perpendicular, or neither. Line 1 and Line 2 : Parallel Perpendicular Neither Line 1 and Line 3 : Parallel Perpendicular Neither Line 2 and Line 3 : Parallel Perpendicular Neither

Ask by Valdez Dawson. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

- Line 1 and Line 2: Neither - Line 1 and Line 3: Neither - Line 2 and Line 3: Parallel

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To determine whether the lines are parallel, perpendicular, or neither, we need to first convert each equation into the slope-intercept form, \(y = mx + b\), where \(m\) is the slope. **Line 1:** \( 4x + 6y = -4\) Solving for \(y\): \[ 6y = -4x - 4 \quad \Rightarrow \quad y = -\frac{2}{3}x - \frac{2}{3} \] So the slope \(m_1 = -\frac{2}{3}\). **Line 2:** \( 2y = -3x + 5\) Solving for \(y\): \[ y = -\frac{3}{2}x + \frac{5}{2} \] So the slope \(m_2 = -\frac{3}{2}\). **Line 3:** \(y = -\frac{3}{2}x + 8\) The slope here is \(m_3 = -\frac{3}{2}\). Now, let's analyze the slopes: - For Line 1 and Line 2: - \( m_1 = -\frac{2}{3} \) and \( m_2 = -\frac{3}{2} \) - Since \(m_1 \cdot m_2 = -\frac{2}{3} \cdot -\frac{3}{2} = 1\), they are **perpendicular**. - For Line 1 and Line 3: - \( m_1 = -\frac{2}{3} \) and \( m_3 = -\frac{3}{2} \) - Again, since \(m_1 \cdot m_3 = -\frac{2}{3} \cdot -\frac{3}{2} = 1\), they are **perpendicular**. - For Line 2 and Line 3: - \( m_2 = -\frac{3}{2} \) and \( m_3 = -\frac{3}{2} \) - Since \(m_2 = m_3\), they are **parallel**. So the answers are: Line 1 and Line 2: **Perpendicular** Line 1 and Line 3: **Perpendicular** Line 2 and Line 3: **Parallel**

Latest Geometry Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy