Question

name:____________________________date:______period:__
slope of parallel & perpendicular lines practice
directions: determine if the two lines are parallel, perpendicular, or neither. show any work.

1. line a contains the points (0, 3) and (3,1)

line b contains the points (-1, 4) and (-7, -5)

1. line q: y= 3x+7

line r: y= 1/3x-10

1. line a: x=4

line b: y=2

1. line g: 3x + 2y=10

line h: y= -3/2x - 5
©lindsay bowd

Explanation:

Problem 1:

Step 1: Find slope of Line A

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). For Line A with points \((0, 3)\) and \((3, 1)\), \( m_A=\frac{1 - 3}{3 - 0}=\frac{-2}{3}=-\frac{2}{3} \).

Step 2: Find slope of Line B

For Line B with points \((-1, 4)\) and \((-7, -5)\), \( m_B=\frac{-5 - 4}{-7 - (-1)}=\frac{-9}{-6}=\frac{3}{2} \).

Step 3: Check parallel or perpendicular

Parallel lines have equal slopes (\( m_A
eq m_B \)), perpendicular lines have slopes that multiply to \(-1\) (\( m_A\times m_B = -\frac{2}{3}\times\frac{3}{2}=-1 \)).

Step 1: Identify slopes

For Line Q (\( y = 3x + 7 \)), slope \( m_Q = 3 \). For Line R (\( y=\frac{1}{3}x - 10 \)), slope \( m_R=\frac{1}{3} \).

Step 2: Check parallel or perpendicular

\( m_Q
eq m_R \), and \( m_Q\times m_R = 3\times\frac{1}{3}=1
eq - 1 \).

Step 1: Analyze slopes

Line A (\( x = 4 \)) is a vertical line (undefined slope), Line B (\( y = 2 \)) is a horizontal line (slope \( 0 \)).

Step 2: Check perpendicular

Vertical and horizontal lines are perpendicular (undefined slope times \( 0 \) is undefined, but by definition, they are perpendicular).

Answer:

Perpendicular

Problem 2: