Download 1 y = mx + c Key words: Linear, function, graph

y = mx + c
Key words: Linear, function, graph
Objectives
•
Plot the graphs of linear functions where y is given
explicitly in terms of x
•
Recognise that equations of the form y=mx+c correspond
to straight line graphs
Instructions for the teacher:
KS3 Framework
page ref: 165
In this activity students are asked to engage with different
functions of the form y = mx + c and to look for the variability
generated with changes in m and c. Also, a link is made to the
characteristics of the table of values for each function.
We are going to look at the function y = 2x + 1.
Press Y=
Type 2
Press X,T,θ,n
Type + 1
Now we look at the table of values:
Press 2nd
Press GRAPH (for Table)
You can display the function by using the cursor to highlight
the header row for Y1:
Press ► (right cursor)
Press ▲ (up cursor)
Question: “What are the numbers in the function?” “What do
the 2 and the 1 represent in the table?” Take some suggestions,
but do not formalise them. Students can formalise their ideas
in the class activity.
Set the window so that the axes are in the correct proportion by
pressing WINDOW and entering the numbers shown.
Now we look at the graph:
Press GRAPH
To display the function and show values of points on the line:
Press TRACE
Use the left ◄ and right ►cursor keys to move along the line.
Question: “What are the numbers in the function?” “What do
the 2 and the 1 represent in the graph?” Take suggestions as
before.
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Answers to student activity sheet:
2.
3.
4.
5.
6.
7.
8.
9. A function of the form y = mx + c represents a straight line.
In the table of values the m means the step or difference between the y values and the
c means the value for x = 0
In the graph the m means the steepness and the c means the value of y where the line
crosses the y axis
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Straight Line Graphs: y = mx + c
First: Reset your TI 83-Plus
• Press 2nd + to get MEM
• Choose 7 (Reset…)
• Choose 1 (All Ram…)
• Choose 2 (Reset)
Explore straight line graphs.
1.
First make sure that you can draw a graph, and look at its table of values:
Set the axes by pressing WINDOW and
entering the numbers shown:
We are going to look at the function y = 2x + 1.
Press Y=
Type 2
Press X,T,θ,n
Type + 1
Now we look at the table of values:
Press 2nd
Press GRAPH (for Table)
Now we look at the graph:
Press GRAPH
Press TRACE and use the arrow keys to look at the
values of the function
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2.
The function y = 2x + 1 has two numbers in it.
(a) Look at the table of values what do you think these two numbers represent
in the table of values?
(b) Look at the graph what do you think these two numbers represent in the
table of values?
(c) Write down you first ideas now. Check your ideas with the other functions
that you look at.
3.
Start again and look at the table and graph for y = 3x + 1
[Note: use the CLEAR key to get rid of the 2x + 1]
4.
Start again and look at the table and graph for y = x + 1
5.
Start again and look at the table and graph for y = 4x + 1
6.
Now look at these functions:
(a) y = 2x + 2
(b) y = 2x – 1
(c) y = 2x + 3
(d) y = 2x – 3
7.
Now look at these functions:
(a) y = x – 1
(b) y = 3x – 1
(c) y = 4x – 1
(d) y = −x – 1
8.
Now look at these functions:
(a) y = −2x + 2
(b) y = −3x + 2
(c) y = −x + 2
(d) y = 2x + 2
9.
The letter m is normally used for number in front of the x.
The letter c is normally used for number after the x.
Update your report about the meaning of the m and the c.
Note: You don’t need to
CLEAR each one – use the
down cursor ▼ to use Y1, Y2,
Y3 and Y4
Use this writing frame if it helps:
A function of the form y = mx + c represents a straight line.
In the table of values the m means ……… and the c means ……..
In the graph the m means ……… and the c means ……….
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