The following pairs of lines should be matched with their descriptions as follows:
- y = 2x/3 + 4 and y = -3x/2 + 9; perpendicular lines.
- y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.
- y = 5x/6 + 8 and y = 5x/6 + 2; parallel lines.
What are parallel lines?
Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.
In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
What are perpendicular lines?
Perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).
The condition for two parallel lines.
In Mathematics, the condition for perpendicularity of two lines is:
m₁ × m₂ = -1
Given the following equations:
y = 2x/3 + 4 and y = -3x/2 + 9; 2/3 × -3/2 = -1.
y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.
y = 5x/6 + 8 and y = 5x/6 + 2; 5/6 = 5/6.
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