Unit 2, Lesson 17
Using Equations for Lines
Accelerated 7
Preparation
Lesson Narrative
The purpose of this lesson is for students to write equations for a line when no slope triangles are given. Students begin by revisiting the meaning of dilations and scale factors. Then students draw dilations of a triangle using the same center but different scale factors. Some students may find a pattern in the resulting coordinates, while others may use the definition of dilations to generalize what happens to a point dilated by any scale factor (MP8).
Students are then given a line with a few labeled points and asked to use what they know about similar triangles to find an equation for the line (MP7). Students practice using this line to test whether given points are also on this line.
- Create an equation of a line with positive slope on the coordinate plane using knowledge of similar triangles.
- Generalize (orally) a process for dilating a slope triangle $ABC$ on a coordinate plane with center of dilation $A$ and scale factor $s$.
- Justify (orally) that a point$ (x,y)$ is on a line by verifying that the values of $x$ and $y$ satisfy the equation of the line.
Let’s write equations for lines.
Required Materials
Activity 1
Activity 2
Activity 3
Required Preparation
Provide access to geometry toolkits.
Provide access to geometry toolkits.
Provide access to geometry toolkits (in particular, a straightedge is helpful).