1. Name:________________________________________________________________________________Date:_____/_____/__________
BRAIN BLITZ/Warm-UP
QUIZ DAY!
Fill-in-the-Table with the missing vocabulary terms: x y
1)__________________
____________________
2)___________________
_____________________
Input
Output
Fill-in-the-blanks: 3)
4) What is the range of the following relation? ) {(-2, 4); (-1, 5); (0, 6); (1, 7)}
R = {______________________}
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!
Are the following relations functions? Answer “yes” or “no.”
5)_____
6) ______
{(-20, -38); (-10, -18); (0, 2); (10, 2)}
7)_____ x y
-30 10 40 70 60
100
Write the equation for each of the below tables (remember the magic # shortcut):
8) ) ) x y -1 1 2 3
___
Equation: x y 1 6 2 11 3 16 4
___
Equation: x y -2 2 -1 1
___
Equation:

2. Linear Equations (Functions)
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!

3. What is it?:
Linear Equation-- equation with ________ different variables and neither variable contains an exponent greater than 1.
For example: y = 3x + 2 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)!

4. examples: x y = 2x - 1 y -1 1 2 y = 2 (-1) – 1 y = -2 – 1 y = -3 -3
Just plug in
the “x” values!
Just plug in
the “x” values!
examples: 1 x
y = 2x - 1 y -1 1 2
y = 2 (-1) – 1
y = -2 – 1
y = -3 -3
y = 2 (0) – 1
y = 0 – 1
y = -1 -1
y = 2 (1) – 1
y = 2 – 1
y = 1 1
y = 2 (2) – 1
y = 4 – 1
y = 3 3

5. 2 x
y = x + 8 y -1 1 2 7 8 9 10
Just plug in
the “x” values!

6. 3
y = 8 – 3x x y -4 -2 2 20 14 8 2
Just plug in
the “x” values!

7. 4
x = y + 6 x y -4 -2 2
-10 -8 -6 -4
Careful. “x” can be anywhere in equation . . .

8. Solve: x + 2y = 4 5 If you aren’t given a table, make one!
It’s okay to have some fraction output (y) values! 5
Solve: x + 2y = 4

9. input /output (x,y) combo represents a point
Remember, every
input /output (x,y) combo represents a point
on the coordinate
plane! 6
Equation:
y = 2 – 3x
Graph:
Table: x y -2 -1 1 8 5 2 -1
Notice the straight line!! It’s no surprise that a linear equation graphs as a straight
line!

10. homework
IXL: 7th Grade, V.5

11. END OF LESSON
The next slides are student copies of the notes/ hand-outs for this lesson. These were handed out in class and filled-in as the lesson progressed.

12. Math-7 NOTES
DATE: ______/_______/_______
NAME:
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 2 x
y = 2x - 1 y -1 1 2 x
y = x + 8 y -1 1 2
y = 2 (-1) – 1
y = -2 – 1
y = -3
y = 2 (0) – 1
y = 0 – 1
y = -1
y = 2 (1) – 1
y = 2 – 1
y = 1
y = 2 (2) – 1
y = 4 – 1
y = 3
Careful. “x” can be anywhere in equation . . . 3
y = 8 – 3x 4 x y -4 -2 2
x = y + 6 x y -4 -2 2

13. Table: (show work below)
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
Graph:
Table: (show work below) x y -2 -1 1
IXL: 7TH Grade, V.5

14. Math-7 PRACTICE/ CLASSWORK
NAME:________________________________________________________________________________ DATE: _____/_____/__________
“Linear functions ”
Solve:
1) )
3) )
Solve (Make your own table, and choose your own x values):
5) y = -8x ) y = -4x - 1 x
y = x + 1 y -1 1 2 x
y = x - 5 y -1 1 2
y = 3x + 2 x y -2 2 4
y = -4x x y
-10 -5 5

15. Solve. Be careful– plug x values in exactly where you see x
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 = 2y - 3 x y -1 1 2 x y -1 1 2 9)
Equation: y = -x + 2
Graph:
Table: (show work below) x y -3 -1 1 3
10)
Equation: y = 3x – 1
Graph:
Table: (show work below) x y -1 1 2

16. “Equations from Patterns”
Math-7 Extra PRACTICE
NAME:__________________________________________________________________________________________________________DATE:_____/_____/__________
Using the pattern in the chart, how many toothpicks would be needed for a
figure with 5 hexagons? __________
Consider the second column of numbers written as a sequence:
6, 11, 16,
Is there a common difference? __________ So, this is an example of
which type of sequence?______________________________________
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: ______________________________________________________

17. Remember the “magic #” shortcut?? Let’s practice!
Name:________________________________________________________________________________Date:_____/_____/__________
Math-7 extra practice
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 #!