Name:________________________________________________________________________________Date:_____/_____/__________
Solve the following linear equations (plug x into equation):
1)
x
y = -2(x + 1)
y
2)
x
-1
-1
0
0
1
1
2
2
x = y-4
y
Write the equation for the following function tables (magic #):
3)
x
y
-1
4)
x
y
-1
0
0
4
1
2
5)
x
y
4
8
29
1
1
9
33
9
2
-2
10
37
14
3
-5
11
41
Equation:____________
Equation:____________
Equation:____________
Fill-in-the-blank:
6) y = mx + b is the formula for writing a linear equation in
________________________________ form.
7) The “m” stands for _________________ .
8) The “b” stands for the _______________________ .
Graph the following equations (use y = mx + b):
9)
y = -3x + 8
( m = _____; b = _____ )
10)
y=
𝟑
x–6
𝟏
( m = _____; b = _____ )
Study graph and write the equation (use y = mx + b):
11)
m = _____
b = _____
Equation:__________________________
NAME:__________________________________________________________________________________ DATE: ______/_______/_______
Math-7 practice
“SLOPE-intercept form”
m = _____
m = _____
b = _____
b = _____
m = _____
m = _____
b = _____
b = _____
m = _____
m = _____
b = _____
b = _____
m = _____
m = _____
b = _____
b = _____
Today’s Lesson:
What:
Representing a function
Why:
To make connections among the four
ways to represent a function.
Input
Output
Do you remember the 4 ways to
represent a function??:
1
As an
y = 2x + 3
Equation
____________
2
With
words
3
As a
Table
__________
4
“y is equal to
two times a number
------------------------plus three.
---------------------”
As a
graph
x
0
1
y
3
5
2
3
7
9
Now, plot
the
points!
let’s tie it all together . . .
From an equation . . .
Equation
1)
Words
y = 2x -1
m=
𝟐
𝟏
b = -1
Table
x
y
0
-1
1
1
2
3
3
5
“y is equal to the product
of two and a number,
minus one.”
Graph
From words . . .
Equation
2)
Words
y=x+3
“y is equal to three
more than a number.”
You could use y= mx + b to
graph OR you could create
the table by choosing inputs
and plugging in . . .
Table
x
0
y
1
4
2
5
3
6
Graph
3
Now, plot the
points!
From a table . . .
Equation
3)
Words
y = -2x + 6
“y is equal to negative 2
times a number,
plus six.”
Table
x
y
0
6
1
4
2
2
3
0
Graph
Magic
Number . . .
From a graph . . .
Equation
4)
Words
y = -2x + 4
m=
−𝟐
𝟏
“y is equal to four
more than negative 2
times a number.”
b=4
Table
x
y
0
4
1
2
2
0
3
-2
Graph
END OF LESSON
The next slides are student copies of the notes and/or
handouts for this lesson. These were handed out in
class and filled-in as the lesson progressed.
NAME:
Math-7 NOTES
DATE: ______/_______/_______
What: representing functions
Why:
To make connections between the four ways to represent functions.
Do you remember the 4 ways to represent a function??:
1
Of course you
remember!
As an
_____________
2
y = 2x + 3
“y is equal to
---------------------------------------------”
With
words
3
x
As a
___________
y
0
1
2
3
4
As a graph
If you are given one of the above representations, you need
To be able to represent that function in the other 3 ways!
Matching representations activity
NAME:________________________________________________________________________________ DATE: _____/_____/__________
Math-7 homework
“Function representations”
Apply everything we have learned in this unit in order to fill in blank spaces:
Equation
Words
Table
Graph
1) y = 2x - 2
“y is equal to
the product of
2 and a
number, minus
2.”
x
y
-1
0
1
2
2) y = -3x + 1
x
y
0
1
2
3
3)
“Four plus a
number is
equal to y.”
x
y
-3
0
3
6
4)
“ y equals
negative x.”
x
0
1
2
3
y
Equation
Words
Table
Graph
5)
x
y
-1
-3
0
1
1
5
2
9
Magic # . . .
6)
x
y
-2
7
-1
4
0
1
1
-2
Magic # . . .
7)
x
y
y = mx + b
8)
x
y
y = mx + b
NAME:__________________________________________________________________________________ DATE: ______/_______/_______
Math-7 classwork
“Linear Equation applications”
It is midnight in Leesburg and there is no snow on the ground. It begins to snow at
a rate of 2 cm each hour.
Create a table that shows the amount of
snow on the ground for every hour after
midnight until 5 am. (Hint: use 0 to
represent midnight)
x
Graph the equation using your table of values:
y
0
1 am
Write an equation to represent this
situation.
If it continues to snow at the same rate, how much
snowfall would there be at 10 am?
Equation:____________________________________
At midnight in Chicago there are 4 cm of snow on the ground. It begins to snow at a
rate of 3 cm per hour.
Create a table that shows the amount of
snow on the ground for every hour after
midnight until 5 am.
x
Graph the equation using your table of values:
y
0
1 am
Write an equation to represent this
situation.
Equation:____________________________________
If it continues to snow at the same rate,. How much
snowfall would there be at 2 pm (14:00)?
Draw and extend the following pattern:
Create a table that shows the relationship
between the figure number and the number
of toothpicks in each figure.
x
Graph the equation using your table of values:
y
Write an equation to represent this situation.
How many toothpicks will be in the 75th figure?
Equation:_________________________________________
Draw and extend the following pattern:
Create a table that shows the relationship
between the figure number and the
number of square blocks in each figure.
x
Graph the equation using your table of values:
y
Write an equation to represent this
situation.
Equation:______________________________________
How many square blocks will be in the 88th
figure?