Student Page 2.7.2 Linear Functions with Desmos β Slopes and y-Intercepts
Use Desmosβ33β to complete the following investigation. Be ready to discuss your findings with your group and with the class.
1.
Type
2.
Set
(a)
(b)
(c)
(d)
What effect does changing
(e)
Why does
3.
Graph the line
4.
(a)
Which line is steeper, one with a slope of 2 or one with a slope of 0.25? Why?
(b)
When
5.
(a)
Which line is steeper, one with a slope of
(b)
When
6.
Let
(a)
What is the equation of the line when
(b)
What is the equation of the line when
(c)
What is the equation of the line when
7.
Set
(a)
(b)
(c)
(d)
What effect does changing
(e)
Which direction is the graph moving, up and down or left and right? How do you know?
8.
(a)
In your own words, what is slope?
(b)
State everything you can about the value of m and the appearance of the graph of
(c)
In your own words, what is the
(d)
State everything you can about the value of
9.
Predict the appearance of the graph of each of the following lines. Do not draw them yet.
(a)
(b)
(c)
(d)
Hold an empty page protector against your computer/tablet screen. Use the viewing window on your screen and hand-draw each graph using a dry erase marker. (Trace the
(e)
Without changing the viewing window, electronically graph each of the equations in Task 2.7.2.9.aβ2.7.2.9.c. Compare the Desmos graphs with your hand-drawn graphs. If any graph is incorrect, decide what caused the error.
10.
Summarize your work. Answer the following questions and any others that occur to you.
(a)
Given a graph, how can you determine its slope?
(b)
In an equation of a line,
(c)
Given a graph, how can you determine its
(d)
In an equation of a line,