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Name:________________________________________________________________________________Date:_____/_____/__________
Fill-in-the-table:
1) Remember the 4 ways to represent a function? They are . . .
Equation
_____________
Table
______________
Solve the following linear equations (plug x into equation):
2) y = 3x – 2
x
y
3) x + y = 8
-1
-1
0
0
1
1
2
2
Multiple Choice:
4) Which equation represents
the following function table?
x
y
-1
-7
0
-2
1
3
2
B. y = 5x
D. y = 5x - 2
Magic # . . .
5) Which equation represents
the following function table?
Can you
use magic
# here??
A. y = x + 5
C. y = x + 6
8
x
y
-5
-20
0
0
5
20
10
40
x
A. y = 20x
B. y = x + 20
C. y = 4x
D. y = 2x + 10
y
6) Which table represents the
following equation?
A.
y = 3x - 1
Plug ALL x
values into
equation
BEFORE you
choose table . . .
7) Which table represents the
following equation?
C.
A.
y = -4x + 1
Plug ALL x
values into
equation
BEFORE you
choose table . . .
C.
x
y
x
y
-1
-4
-1
-4
0
--1
0
--1
1
2
1
2
2
6
2
5
x
y
x
y
-1
2
-1
-4
0
-1
0
-1
1
2
1
2
2
5
2
7
x
y
0
1
1
B.
D.
x
y
0
1
-3
1
-3
2
-7
2
-9
3
-12
3
-13
x
y
x
y
-2
9
-5
21
0
1
-2
9
2
-7
1
-3
4
-15
4
-17
B.
D.
Today’s Lesson:
What:
Graphing linear equations
Why:
To use “slope-intercept form” in order to
graph linear equations.
y = mx + b
Remember . . .
A linear equation is an equation with 2
different variables (like y = 4x + 1 )– with
no exponents. Also, they graph as a
___________________
line!
straight
Well, when a linear equation is written in
a specific order/ format, we call it slope-
intercept form . . .
In other words, when the equation is
written like this:
y = 5x + 2
Y is isolated on
one side, and the
x term comes
before the
constant!
The slope-intercept formula is: y= mx + b
What is y = mx + b ??
Well, the m variable stands for ____________,
slope
& the b variable stands for the y-intercept.
steep
slope – measure of how ______________
a line
is. It is often described as a ratio of a line’s
𝑟𝑖𝑠𝑒 (𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒)
rise over its run –(
).
𝑟𝑢𝑛 (ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒)
y-intercept– point where the line crosses
the ____________________
.
y axis
Consider the
diagram . . .
Let’s apply it . . .
1)
y = mx + b
y = 3x + 2
Step 1:
Identify the “m” and the “b” :
𝟑
m = 3 or
𝟏
b=2
Step 2: Plot the y-intercept or b
Step 3: Apply slope--rise 3 and run 1 . . .
Positive slopes
will always
graph as
UPHILL lines!
2)
y = -4x + 6
y = mx + b
m = -4
b= 6
Negative slopes will
always graph as
DOWNHILL lines!
When the slope is
negative, we FALL
instead of RISE . . .
3)
y=
𝟏
x
𝟐
m=
-3
𝟏
𝟐
b = -3
y = mx + b
What if we have the graph Only??
We can easily use “y = mx + b” to come up with
the equation as well!
How?
Study the graph of the line. Identify the y-intercept
____________
(where it crosses the y axis). This is the “b.”
Then, determine the slope. Is it an uphill or a
downhill? This tells you whether the slope is
positive or ___________.
negative Count the “rise” grid moves
versus the “run” grid moves. This is the “m.”
𝟑
4) m = - 𝟒
b = -2
So, the equation
is . . .
𝟑
y = - 𝟒 x + (-2)
________________
Downhill means
negative slope!
5)
Uphill means
positive slope!
y = mx + b
m=
𝟐
𝟏
b= 2
y = 2x + 2
So, the equation is . . . ________________
6)
Downhill means
negative slope!
y = mx + b
m= -
𝟏
𝟓
b = -3
𝟏
y = - 𝟓 x + (-3)
So, the equation is . . .________________
END OF LESSON
The next slides are student copies of the notes for this
lesson. These notes were handed out in class and
filled-in as the lesson progressed.
NOTE: The last slide(s) in any lesson slideshow
represent the homework assigned for that day.
NAME:
Math-7 NOTES
DATE: ______/_______/_______
What: Graphing linear equations
Why: To use “slope-intercept form” in order to graph linear equations.
A linear equation is an equation with 2 different variables
(like y = 4x + 1 )– with no exponents. Also, they graph as a
___________________ line!
Well, when a linear equation is written in a specific order/ format, we call it slopeintercept form . . . In other words, when the equation is written like this: y = 5x + 2
The slope-intercept formula is:
y= mx + b
Y is isolated on one side,
and the x term comes
before the constant!
What is y = mx + b ??
Well, the m variable stands for _________________________, & the b variable stands for the y-intercept.
slope – measure of how ______________ a line is. It is often described as a ratio of a line’s rise over its
𝑟𝑖𝑠𝑒 (𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒)
run –( 𝑟𝑢𝑛 (ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒) ).
y-intercept– point where the line crosses the _____________________________________ .
Consider the
diagram . . .
What if we have the graph Only??
We can easily use “y = mx + b” to come up with the equation as well!
How?
Study the graph of the line. Identify the ____________ (where it crosses the y axis). This is the “b.”
Then, determine the slope. Is it an uphill or a downhill? This tells you whether the slope is positive
or __________________. Count the “rise” grid moves versus the “run” grid moves. This is the “m.”
_________
_________
NAME:________________________________________________________________________________ DATE: _____/_____/__________
Math-7 CLASSWORK
“Function representations”
Apply everything we have learned in this unit in order to fill in blank spaces:
Equation
Words
Table
Graph
1) y = 3x - 2
“y is equal to
the product of
3 and a
number, minus
2.”
x
y
-1
0
1
2
2) y = x – 4
x
y
0
1
2
3
3)
“Three more
than a number
is equal to y.”
x
y
-3
0
3
6
4)
“ y equals twice
a number,
decreased by
3.”
x
0
1
2
3
y
Equation
Words
Table
Graph
5)
x
y
-1
-4
0
-1
1
2
2
5
Magic # . . .
6)
x
y
-1
-1
0
1
1
3
2
5
Magic # . . .
7)
x
y
0
1
2
3
y = mx + b
8)
x
y
-1
0
1
2
y = mx + b
NAME:________________________________________________________________________________ DATE: _____/_____/__________
Math-7 Homework
Graph the following equations (use y = mx + b):
1)
y = -4x + 7
3)
y=
3
2
x -5
( m = _____; b = _____ )
( m = _____; b = _____ )
2)
4)
y=
2
x–4
( m = _____; b = _____ )
y=- x+8
( m = _____; b = _____ )
3
1
2
Study graphs and write the equation (use y = mx + b):
5)
( m = _____; b = _____ )
6)
Equation:____________________________
7) ( m = _____; b = _____ )
Equation:____________________________
( m = _____; b = _____ )
Equation:_____________________________
8)
( m = _____; b = _____ )
Equation:_____________________________