Lesson 9
Equations of Lines
Lesson Narrative
In grade 8, students used similar triangles to explain why the slope \(m\) is the same between any two distinct points on a nonvertical line in the coordinate plane, and they derived the equation \(y = mx + b\) for a line intercepting the vertical axis at \(b\). In this lesson, students develop the pointslope form of a linear equation: \(yk=m(xh)\). Students will be writing equations of lines in the next several lessons, and intercepts will not always be readily available. Pointslope form will require the least algebraic manipulation and allow students to focus on geometric properties.
Slope calculations are an important part of this lesson, so students begin with a warmup that helps them recall this concept. Then they use the definition of slope to build the pointslope equation, mirroring the way they developed the equation of a circle. Finally, they practice writing and interpreting equations of lines in pointslope form. Students have the opportunity to construct a viable argument (MP3) when they explain their methods of calculating slope.
Learning Goals
Teacher Facing
 Generalize (using words and other representations) that a line can be represented by an equation in pointslope form.
Student Facing
 Let’s investigate equations of lines.
Required Preparation
Set up a display for graphing technology so you can dynamically graph several studentgenerated equations, both in one of the activities and in the lesson synthesis.
Learning Targets
Student Facing
 I can use the definition of slope to write the equation for a line in pointslope form.
CCSS Standards
Glossary Entries

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