Lesson 8Translating to y=mx+b
Learning Goal
Let’s see what happens to the equations of translated lines.
Learning Targets
I can explain where to find the slope and vertical intercept in both an equation and its graph.
I can write equations of lines using y=mx+b.
Lesson Terms
- linear relationship
- vertical intercept
Warm Up: Lines that Are Translations
Problem 1
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
under a translation? For each line that is a translation of
, draw an arrow on the grid that shows the vertical translation distance.
Activity 1: Increased Savings
Problem 1
Diego earns $10 per hour babysitting. Assume that 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? Write an equation for each line.
Print Version
Diego earns $10 per hour babysitting. Assume that 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? Write an equation for each line.
Activity 2: Translating a Line
Problem 1
Experiment with moving point
. Place point
in three different locations above the -axis. For each location, write the equation of the line and the coordinates of point . Place point
in three different locations below the -axis. For each location, write the equation of the line and the coordinates of point . In the equations, what changes as you move the line? What stays the same?
If the line passes through the origin, what equation is displayed? Why do you think this is the case?
Your teacher will give you 12 cards. There are 4 pairs of lines, A–D, showing the graph,
, of a proportional relationship and the image, , of under a translation. Match each line with an equation and either a table or description. For the line with no matching equation, write one on the blank card.
Print Version
This graph shows two lines. Line
Select all of the equations whose graph is the line
. -
Your teacher will give you 12 cards. There are 4 pairs of lines, A–D, showing the graph,
, of a proportional relationship and the image, , of under a translation. Match each line with an equation and either a table or description. For the line with no matching equation, write one on the blank card.
Are you ready for more?
Problem 1
A student says that the graph of the equation
Lesson Summary
During an early winter storm, the snow fell at a rate of
In addition to being a linear relationship between the time since the beginning of the storm and the depth of the snow, we can also call this as a proportional relationship since the depth of snow was 0 at the beginning of the storm.
During a mid-winter storm, the snow again fell at a rate of
Two hours after each storm begins, 1 inch of new snow has fallen. For the first storm, this means there is now 1 inch of snow on the ground. For the second storm, this means there are now 6 inches of snow on the ground.
Unlike the first storm, the second is not a proportional relationship since the line representing the second storm has a vertical intercept of 5. The equation representing the storm,