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Unit 5, Lesson 7

Translating to

Accelerated 7

7.1

Warm-up

Lines that Are Translations

Standards Alignment

Building On

Addressing

Building Toward

The diagram shows several lines. You can only see part of the lines, but they actually continue forever in both directions.

Lines j, h, g, f, e graphed on grid. j is green, h is yellow, g is blue, f is black, and e is red.

Which lines are images of line after a translation?
For each line that is a translation of , draw an arrow on the grid that shows the vertical translation distance.

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7.2

Activity

Increased Savings

Standards Alignment

Building On

Addressing

Building Toward

Diego earns $10 per hour babysitting. He has no money saved before he starts babysitting and plans to save all of his earnings. Graph how much money, , he has after hours of babysitting.
Now imagine that Diego started with $30 saved before he starts babysitting. On the same set of axes, graph how much money, , he would have after hours of babysitting.
Compare the second line with the first line. How much more money does Diego have after 1 hour of babysitting? 2 hours? 5 hours? hours?

7.3

Activity

Translating a Line

Standards Alignment

Building On

Addressing

Building Toward

Your teacher will give you a set of cards containing 4 graphs showing line

and its image, line

, after a translation. Match each graph with an equation describing the translation and either a table or description. Record your matches and be prepared to explain your reasoning. For the line with no matching equation, write one on the blank card.

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Student Lesson Summary

During an early winter storm, snow falls at a rate of inch per hour. The rate of change, , can be seen in both the equation and in the slope of the line representing this storm.

The time since the beginning of the storm and the depth of the snow is a linear relationship. This is also a proportional relationship since the depth of snow is 0 inches at the beginning of the storm.

Graph of line. Horizontal axis, time since beginning of storm in hours, scale 0 to 6, by 1’s. Vertical axis, depth of snow in inches, scale 0 to 9, by 1’s.

During a mid-winter storm, snow again falls at a rate of inch per hour, but this time there were already 5 inches of snow on the ground.

Graph of 2 lines. Points plotted on one line include 2 comma 6 and 4 comma 7. Points plotted on other line include 2 comma 1 and 4 comma 2. Arrows drawn between points.

The rate of change, , can still be seen in both the equation and in the slope of the line representing this second storm.

The 5 inches of snow that were already on the ground can be graphed by translating the graph of the first storm up 5 inches, resulting in a vertical intercept at . It can also be seen in the equation .

This second storm is also a linear relationship, but unlike the first storm, is not a proportional relationship since its graph has a vertical intercept of 5.

Glossary

None

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Lesson

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Assessment Access

Translating to

Warm-up

Lines that Are Translations

Standards Alignment

8.G.1

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Activity

Increased Savings

Standards Alignment

8.G.1.c

8.EE.B

Activity

Translating a Line

Standards Alignment

8.G.1.c

8.EE.B

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Student Lesson Summary

Glossary

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