Translating to $y=mx+b$
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to remind students that the translation of a line is parallel to the original line. They begin by inspecting several lines to decide which are translations of a given line. Students then describe the translations by specifying the number of units and the direction, in preparation to see the equation y=mx+b as a translation of y=mx.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet think time and access to geometry toolkits. Ask them to share their responses with a partner afterwards.
Student Task
The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.
- Which lines are images of line f after a translation?
- For each line that is a translation of f, draw an arrow on the grid that shows the vertical translation distance.
Sample Response
- Lines h and e. Sample reasoning: They are parallel to line f, and translated lines are parallel to the original.
- Line h is line f translated up 6 units. Line e is line f translated down 2 units.
Activity Synthesis (Teacher Notes)
Invite students to share how they determined that lines h and e are translations of f. Emphasize that lines h and e are parallel to f, and line f matching up with the other lines would require a rotation or reflection. If possible, demonstrate the transformations using a clear transparency or tracing paper. If using a transparency or tracing paper to demonstrate the translations, it is helpful to draw a dot for a specific point on both the underlying graph and on the transparency as a reference point.
Standards
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations:
15 min
15 min
Knowledge Components
All skills for this lesson
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Translating to $y=mx+b$
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to remind students that the translation of a line is parallel to the original line. They begin by inspecting several lines to decide which are translations of a given line. Students then describe the translations by specifying the number of units and the direction, in preparation to see the equation y=mx+b as a translation of y=mx.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet think time and access to geometry toolkits. Ask them to share their responses with a partner afterwards.
Student Task
The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.
- Which lines are images of line f after a translation?
- For each line that is a translation of f, draw an arrow on the grid that shows the vertical translation distance.
Sample Response
- Lines h and e. Sample reasoning: They are parallel to line f, and translated lines are parallel to the original.
- Line h is line f translated up 6 units. Line e is line f translated down 2 units.
Activity Synthesis (Teacher Notes)
Invite students to share how they determined that lines h and e are translations of f. Emphasize that lines h and e are parallel to f, and line f matching up with the other lines would require a rotation or reflection. If possible, demonstrate the transformations using a clear transparency or tracing paper. If using a transparency or tracing paper to demonstrate the translations, it is helpful to draw a dot for a specific point on both the underlying graph and on the transparency as a reference point.
Standards
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations: