Translating to y = mx + b

Interact with the slider in the applet below.


Match Graphs and Tables of Linear Relationships.

There are 4 pairs of lines, A–D, showing the graph, a, of a proportional relationship and the image, h, of a under a translation. Match each line h with an equation and either a table or description.

(1). For the line with no matching equation, write one.

(2). If the line passes through the origin, what equation is displayed?


Use Graphs to Solve Problems Involving Linear Relationships.

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.

(1). Graph how much money, , he has after hours of babysitting.

Now imagine that Diego started with $30 saved before he starts babysitting.

(2). 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.

(3). How much more money does Diego have after 1 hour?

(4). How much more money does Diego have after 2 hours?

(5). How much more money does Diego have after 5 hours?

(6). How much more money does Diego have after hours?

(7). Write an equation for each line.


Observe the Movement of a Straight Line on the Coordinate Plane.

Experiment with moving point A.

Place point A in three different locations above the  -axis.

(1). For each location, write the equation of the line and the coordinates of point A.

(2). In the equations, what changes as you move the line?

(3). What stays the same?

(4). Why do you think this is the case?


Match each graph to a situation.


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

(1). Which lines are images of line under a translation?

(2). For each line that is a translation of f, draw an arrow on the grid that shows the vertical translation distance.


Select all the equations that have graphs with the same -intercept.