KnowledgeMadeFun, home

Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Parallel and perpendicular lines: equal slopes and negative reciprocals

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 5 s
  • British Columbia
  • BC10-MA-17

Using y = 2/3x + 1, the video shows that y = 2/3x − 4 is parallel because it has the same slope. It then shows that a perpendicular slope is the negative reciprocal, checked by 2/3 × (−3/2) = −6/6 = −1, works out the perpendicular line through (2, 0) as y = −3/2x + 3, marks the right angle on the grid, and shows the common mistake of flipping the fraction without changing the sign, which gives 2/3 × 3/2 = 1, not −1.

Anyone can watch two lessons on the website without an account. Signing in is free, no payment and no card, and opens three a day; Plus has no limit.

Loading

Share to Google Classroom

In one sentence

The question this lesson answers

When are two lines parallel, and when are they perpendicular? Their slopes tell us.

In y equals m x plus b, m is the slope, or rise over run, and b is the y-intercept, where the line crosses the y-axis.

Transcript

What the lesson says

When are two lines parallel, and when are they perpendicular? Their slopes tell us.

In y equals m x plus b, m is the slope, or rise over run, and b is the y-intercept, where the line crosses the y-axis.

Our first line is y equals two thirds x plus 1. Its slope is two thirds: a run of 3, a rise of 2.

Parallel lines never meet. Now draw y equals two thirds x minus 4.

It has the same slope, so the gap never closes. Different lines with equal slopes are parallel.

Perpendicular lines meet at a right angle. If neither line is vertical, their slopes are negative reciprocals.

For a negative reciprocal, flip the fraction, then change the sign: two thirds becomes negative three halves.

Check: two thirds times negative three halves is negative six sixths, or negative 1.

Now find the perpendicular to our first line through the point 2, 0.

Its slope is negative three halves, so y equals negative three halves x plus b. Put in 2 for x and 0 for y.

Negative three halves times 2 is negative 3, so 0 equals negative 3 plus b, and b equals 3.

So the line is y equals negative three halves x plus 3, and it meets our first line at a right angle.

A common mistake is to flip without changing the sign. Two thirds times three halves is 1, not negative 1: not perpendicular.

Recap: equal slopes give parallel lines, and negative reciprocal slopes give perpendicular lines.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Linear relations: linear functions: slope and equations of linesBC10-MA-17

Previous: General form, and changing between the forms of a lineNext: Horizontal and vertical lines: y = 3 and x = −2

The outcomes and strands follow the British Columbia curriculum.

Keep going

More on this topic