Using Parallel and Perpendicular Lines
Write equations of parallel and perpendicular lines in Grade 10 using slope relationships: parallel lines share slopes while perpendicular slopes multiply to -1.
Key Concepts
New Concept For parallel lines: $m 1 = m 2$. For perpendicular lines: $m 1 m 2 = 1$.
Why it matters Algebra is the language that translates geometric relationships, like parallel and perpendicular lines, into precise numerical rules you can manipulate. This bridge between visual shapes and symbolic equations is fundamental to everything from video game design to engineering complex structures.
What’s next Next, you'll use these slope rules to write equations for new lines and prove geometric properties, like whether a triangle is a right triangle.
Common Questions
What is the slope relationship for parallel lines?
Parallel lines have equal slopes (m₁ = m₂) but different y-intercepts. They never intersect.
What is the slope relationship for perpendicular lines?
Perpendicular lines have slopes that are negative reciprocals of each other: m₁ × m₂ = -1. If one slope is 2/3, the perpendicular slope is -3/2.
How do you write the equation of a line perpendicular to y=3x+1 through (0,2)?
The perpendicular slope is -1/3 (negative reciprocal of 3). Using y=mx+b with point (0,2): y = -x/3 + 2.