8 Translating to y = mx + b

8 Translating to

y = mx + b

Remember that a TRANSLATION is a slide. To translate an object, slide it!

Multiple Choice

Which transformation is a translation?

• A

• B

• C

• D

Multiple Select

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 under a translation?

• g

• h

• i

• j

 

Lines h and i are translations of line f.

They appear to be parallel to f, and translated lines are parallel to the original.

h is f translated up 6 units. i is f translated down 2 units.

Graph it!

Now let's graph the relationship between how many hours Diego works and how much he is paid. The axes are labeled on the right. On the next slide, I will ask you to choose points that will be on the graph.

Multiple Select

We said Diego earns $10 an hour babysitting and represented the amount he earns (y) based on the number of hours he works (x) with the equation y = 10x. Which of the following points could be on the graph of this equation?

• (0, 0)

• (10, 1)

• (2, 20)

• (5, 25)

• (7, 70)

You're doing an awesome job!

Here's what the graph to represent this situation looks like...

Multiple Select

In the equation y = 10x, what does the 10 represent in this situation? Select all that apply!

• Diego is 10 years old.

• Diego gets paid $10 per hour.

• Diego works for 10 hours.

• The slope of the line.

• The y-intercept of the line.

Open Ended

What if Diego has $30 in savings before he starts babysitting? How will this affect the graph? Will it change the slope of the line? Will it change the y-intercept of the line? What do you think???

Multiple Select

We are still thinking about how much money Diego will have if he earns $10 an hour babysitting. This time, however, let's calculate his total given that he already has $30. Which points could appear on this graph?

• (0, 30)

• (1, 10)

• (2, 50)

• (3, 30)

• (5, 80)

Here's how the new line would look. (It's the one in blue!) Notice that it's a translation of the first line we looked at.

Multiple Choice

So, if the equation to represent the amount of money Diego has was originally written as y = 10x, what is the equation to represent how much he has if he starts with $30 and then earns $10 for each hour worked?

• y = 10x

• y = 30x

• y = 10x + 30

• y = 30x + 10