# 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.

### Student Facing

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

### 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 $$y = k + m(x-h)$$.

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