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Classify the lines: Line 1 has the equation y = 3x + 5. Line 2 has the equation y - 4 = 3(x- 2). intersecting but not perpendicular coinciding O perpendicular O parallel

Classify the lines: Line 1 has the equation y = 3x + 5. Line 2 has the equation y - 4 = 3(x- 2). intersecting but not perpendicular coinciding O perpendicular O parallel

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Classify the Lines** Line 1 has the equation \( y = 3x + 5 \). Line 2 has the equation \( y - 4 = 3(x - 2) \). **Options:** - ○ intersecting but not perpendicular - ○ coinciding - ○ perpendicular - ○ parallel To determine the relationship between these two lines, solve for the equation of Line 2: 1. Expand Line 2's equation: \( y - 4 = 3(x - 2) \) \( y - 4 = 3x - 6 \) Add 4 to both sides: \( y = 3x - 2 \) 2. Compare the equations: - Line 1: \( y = 3x + 5 \) - Line 2: \( y = 3x - 2 \) Since both lines have the same slope of 3 and different y-intercepts, they are parallel.
Transcribed Image Text:**Classify the Lines** Line 1 has the equation \( y = 3x + 5 \). Line 2 has the equation \( y - 4 = 3(x - 2) \). **Options:** - ○ intersecting but not perpendicular - ○ coinciding - ○ perpendicular - ○ parallel To determine the relationship between these two lines, solve for the equation of Line 2: 1. Expand Line 2's equation: \( y - 4 = 3(x - 2) \) \( y - 4 = 3x - 6 \) Add 4 to both sides: \( y = 3x - 2 \) 2. Compare the equations: - Line 1: \( y = 3x + 5 \) - Line 2: \( y = 3x - 2 \) Since both lines have the same slope of 3 and different y-intercepts, they are parallel.
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