Lesson 12

It’s All on the Line

Lesson Narrative

In this lesson, students have the opportunity to attend to precision in thinking and language (MP6) as they determine what information is needed to graph a line and ask precise questions to elicit that information. Then, they apply concepts of parallel and perpendicular lines to conclude that if two lines are both perpendicular to the same line, they must be parallel.

Learning Goals

Teacher Facing

  • Determine what information is needed to write the equation of a line and ask (orally) questions to elicit that information.

Student Facing

  • Let’s work with both parallel and perpendicular lines.

Learning Targets

Student Facing

  • I can gather information about a line and write its equation.

CCSS Standards

Glossary Entries

  • opposite

    Two numbers are opposites of each other if they are the same distance from 0 on the number line, but on opposite sides.

    The opposite of 3 is -3 and the opposite of -5 is 5.

  • point-slope form

    The form of an equation for a line with slope \(m\) through the point \((h,k)\). Point-slope form is usually written as \(y-k = m(x-h)\). It can also be written as \(y = k + m(x-h)\).

    A line with point h comma k on an x y axis.
  • reciprocal

    If \(p\) is a rational number that is not zero, then the reciprocal of \(p\) is the number \(\frac{1}{p}\).