Math 1 · Unit 4 · Lesson 3

Same, Parallel, or Perpendicular?

Put the two ideas together. Given two lines as equations, graphs, or pairs of points, compare their slopes: equal slopes mean parallel, unless the y-intercepts match too and it is the same line; slopes that multiply to negative one mean perpendicular; anything else is neither. Then choose the right move yourself to write a parallel or perpendicular line through a point.

About 35 minutes One decision, in order

The big idea

Everything in this unit is one number, the slope, read two ways. Get both slopes, however the lines are given. If they are equal, the lines are parallel, unless the y-intercepts are equal too, in which case they are one line. If the slopes multiply to negative one, the lines are perpendicular, with the horizontal and vertical pair handled by sight. Anything else is neither. And writing a line through a point that is parallel or perpendicular to a given line is the same two moves every time; only the first move changes: keep m for parallel, take the negative reciprocal for perpendicular. Then put the point in and find b.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2One decision, in orderTwo lessons, one number. 3Choose the move: parallel or perpendicular through a pointNow the mixed skill: write a line parallel or perpendicular to a given line through a point, choosing the... 4Sort themTen pairs. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the four-step decision, the four cases, the two moves side by side, and a worked classification. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Perpendicular Lines and the Negative ReciprocalThe slope's second new job. Next lesson: Using Slopes to Check ShapesSlope proves shapes: rectangles and right triangles from their corner points. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.