Name:________________________________________________________________________________Date:_____/_____/__________
QUIZ
DAY!
Fill-in-the-Table with the missing vocabulary terms:
x
y
1)__________________
____________________
2)___________________
_____________________
Input
Output
Fill-in-the-blanks:
3)
Function
A special type of ____________ where there is one and
only one range (y) value for every domain (x) value. In
other words, x can NOT repeat!
4) What is the range of the following relation? ) {(-2, 4); (-1, 5); (0, 6); (1, 7)}
R = {______________________}
Are the following relations functions? Answer “yes” or “no.”
5)_____
x
y
-30
10
0
40
-30
70
60
100
6) ______
7)_____
{(-20, -38); (-10, -18); (0, 2); (10, 2)}
Write the equation for each of the below tables (remember the magic # shortcut):
8)
x
y
0
-1
1
x
y
-2
2
11
-1
0
3
16
0
-2
4
___
1
___
x
y
1
6
1
2
2
3
3
___
Equation:
9)
Equation:
10)
Equation:
Today’s Lesson:
What:
Linear Equations (Functions)
Why:
To solve linear equations, and to graph
the result on the coordinate plane.
Just plug in
the “x” values!
What is it?:
2
Linear Equation-- equation with ________
different variables and neither variable
contains an exponent greater than 1.
For example: y = 3x + 2
In the following examples, you will see
that the equation is given to you– this is
the function rule. You will also see that
the inputs (x values) are given to you.
To solve, we simply “plug” the inputs (x)
into the equation. The result is the
output (or y values)!
Just plug in
the “x” values!
examples:
1
x
-1
0
1
2
y
y
y
y
y
y
y
y
y
y
y
y
y = 2x - 1
= 2 (-1) – 1
= -2 – 1
= -3
= 2 (0) – 1
=0–1
= -1
= 2 (1) – 1
=2–1
=1
= 2 (2) – 1
=4–1
=3
y
-3
-1
1
3
2
x
y= x+8
y
-1
7
0
8
1
9
2
10
Just plug in
the “x” values!
3
y = 8 – 3x
Just plug in
the “x” values!
x
y
-4
20
-2
14
0
8
2
2
4
x= y+6
Careful. “x” can
be anywhere in
equation . . .
x
y
-4
-10
-2
-8
0
-6
2
-4
If you aren’t given a
table, make one!
It’s okay to have
some fraction output
(y) values!
5
Solve: x + 2y = 4
6
Equation:
y = 2 – 3x
Table:
x y
Remember, every
input /output (x,y) combo
represents a point
on the coordinate
plane!
Graph:
8
5
0 2
1 -1
-2
-1
Notice the straight
line!! It’s no surprise
that a linear equation
graphs as a straight
line!
homework
IXL: 7th Grade,
V.5
END OF LESSON
The next slides are student copies of the notes/ handouts for this lesson. These were handed out in class
and filled-in as the lesson progressed.
NAME:
DATE: ______/_______/_______
Math-7 NOTES
What: Linear Equations (Functions)
Why:
To solve linear equations, and to graph the result on the coordinate plane.
Linear Equation-- equation with ________ different variables and neither variable
contains an exponent greater than 1. For example: y= 3x + 2
Just plug in
the “x” values!
In the following examples, you will see that the
equation is given to you– this is the function rule. You
will also see that the inputs (x values) are given to
you. To solve, we simply “plug” the inputs (x) into the
equation. The result is the output (or y values)!
Examples:
1
3
x
y = 2x - 1
-1
y = 2 (-1) – 1
y = -2 – 1
y = -3
-1
0
y = 2 (0) – 1
y =0–1
y = -1
0
1
y = 2 (1) – 1
y =2–1
y =1
1
2
y = 2 (2) – 1
y =4–1
y =3
2
y = 8 – 3x
y
2
x
y= x+8
y
Careful. “x” can be
anywhere in equation . . .
x
y
4
x= y+6
x
-4
-4
-2
-2
0
0
2
2
y
If you aren’t given a table,
make one!
It’s okay to have some
fraction output (y) values!
5
Solve: x + 2y = 4
Solve AND Graph:
6
Equation: y = 2 – 3x
Table: (show work below)
Graph:
x
y
-2
-1
0
1
IXL: 7TH Grade, V.5
NAME:________________________________________________________________________________ DATE: _____/_____/__________
Math-7 PRACTICE/ CLASSWORK
Solve:
1)
3)
x
y=x+1
y
2)
x
-1
-1
0
0
1
1
2
2
y = 3x + 2
x
y
y= x-5
4) y = -4x
y = -8x
x
-2
-10
0
-5
2
0
4
5
Solve (Make your own table, and choose your own x values):
5)
y
6)
y = -4x - 1
y
Solve. Be careful– plug x values in exactly where you see x. You will then need to
solve for y.
7)
x=y+2
x
8)
y
x
-1
-1
0
0
1
1
2
2
9) Equation: y = -x + 2
Table: (show work below)
Graph:
x
y
-3
-1
1
3
10) Equation: y = 3x – 1
Table: (show work below)
x = 2y - 3
Graph:
x
-1
0
1
2
y
y
NAME:__________________________________________________________________________________________________________DATE:_____/_____/__________
Math-7 Extra PRACTICE
“Equations from Patterns”
1.
Using the pattern in the chart, how many toothpicks would be needed for a
figure with 5 hexagons? __________
2.
Consider the second column of numbers written as a sequence:
6, 11, 16, 21 . . .
Is there a common difference? __________ So, this is an example of
which type of sequence?______________________________________
3.
How many toothpicks would be needed for a figure with 10 hexagons?_____
4. If the Number of Hexagons column represents “x” and the Number of
Toothpicks column represents “y,” write an equation that describes how
many toothpicks we would need for any number of hexagons.
Equation: ______________________________________________________
Name:________________________________________________________________________________Date:_____/_____/__________
Remember the “magic
#” shortcut?? Let’s
practice!
TRICKY! Can’t use the
shortcut here because “y” is
NOT increasing by same #!
TRICKY! Can’t use the shortcut
here because “y” is NOT
increasing by same #!