2. how would you translate the graph of y = -x? to produce the graph of y =)?
a. translate the graph of y = -x' up 6 units
b. none of these
c. translate the graph of y = -x? down 6 units
d. translate the graph of y = -x right 6 units
e. translate the graph of y = -x? left 6 units

The purpose of this warm-up is for students to reason about the values we can assign graphs based on which feature of the graph, such as slope and -intercept, the viewer focuses on. Since there are no numbers on the graph, it is important for students to explain how they know the sign of the slope and -intercept based on the position of the graph.

Launch

Display the three graphs for all to see. Tell students that all three graphs have the same scale. Give students 1–2 minutes of quiet work time, followed by a whole-class discussion.

Student Facing

Diego said that these graphs are ordered from smallest to largest. Mai said they are ordered from largest to smallest. But these are graphs, not numbers! What do you think Diego and Mai are thinking?

Three graphs. First line crosses the y axis above the origin, slopes down & right. Second, a horizontal line lies above the x-axis. Third line crosses the y axis below the origin, slopes up & right.

Student Response

Student responses to this activity are available at one of our IM Certified Partners

Activity Synthesis

Display the three graphs for all to see. Invite students to share what they think Diego and Mai are thinking. Encourage students to reference the graphs in their explanation. Record and display their responses for all to see. Emphasize that even though there are no numbers shown, we can tell the sign of the slope and the sign of the -intercept based on the position of the line.

Step-by-step explanation:

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation:

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: