Pre-Algebra
Name _______________________________
Graphing Algebraic Relationships notes
--------------------------------------------------------------------------------------------------------------------------------------In chapter 3 you learned how to solve and graph one-step and two-step equations. Problems you solved looked like
the following:
One-step equation:
𝑥 + 4 = −6
‒4 ‒4
_____________
x = ‒10
𝑥
Two-step equation:
2
− 6 = −2
+6 +6
__________________
2 𝑥
∙ = 4∙2
1 2
x=8
--------------------------------------------------------------------------------------------------------------------------------------Today’s lesson is on the topic of graphing an algebraic relationship. It is an equation that contains ____ variables:
x and y and its graph is a series of points graphed on the ______________________ _______________.
The x-axis is the _________________ number line.
The y-axis is the _________________ number line.
Order pairs are written in the form _____________.
The ______________ is located at (0, 0).
There are 4 _____________ that are labeled counterclockwise.
Plot the following ordered pairs on the coordinate plane.
A (4, 2)
D (2, -4)
B (-3, 3)
E (0, 5)
C (-5, -1)
F (-3, 0)
Ex 1: Graph the following algebraic relationship.
y=x
x
Step 1: Create a table of values. YOU pick
the values of x and then substitute them into
the given equation to find the y.
y
(x, y)
-2
-1
At least five values must be used: (2)
negative, zero, and (2) positive.
0
Step 2: The x and y values form the ordered
pairs you will graph on the Coordinate Plane.
2
1
Step 3: Graph the ordered pairs and connect.
Step 4: Describe the graph.
Describe the graph:
____________________________________________________________________________________________
____________________________________________________________________________________________
Ex 2: Graph the following algebraic relationship.
x
y   1
2
Step 1: Create a table of values. YOU pick
the values of x and then substitute them into
the given equation to find the y.
At least five values must be used: (2)
negative, zero, and (2) positive.
Step 2: The x and y values form the ordered
pairs you will graph on the Coordinate Plane.
Show Work:
x
y
(x, y)
-4
-2
0
2
4
Step 3: Graph the ordered pairs and connect.
Step 4: Describe the graph.
Describe the graph:
____________________________________________________________________________________________
____________________________________________________________________________________________
Graphing Algebraic Relationships HW
Name ________________________________
For each of the following algebraic relationships, make a table of values, write the ordered pairs, graph the ordered
pairs (aka the solution) on the Coordinate Plane, and describe the graph.
2) y = ‒2x
1) y = 2x
x
-2
-1
0
1
2
y
(x, y)
x
y
3) y = x + 2
(x, y)
x
y
(x, y)
1) ____________________
2) _______________________
3) _______________________
______________________
_________________________
__________________________
______________________
_________________________
__________________________
(Hint: For the following algebraic relations that contain division, choose values of x that are divisible by the
divisor number. For example in problem 4, you may choose values for x such as ‒4, ‒2, 0, 2, 4.)
4) y =
x
𝑥
5) y =
2
y
(x, y)
x
𝑥
−3
y
(x, y)
4) _____________________
5) _____________________
_______________________
________________________
_______________________
________________________
𝑥
7) y = x ‒ 1
6) y = 2 − 1
x
y
(x, y)
x
y
8) y = ‒2x + 1
x
(x, y)
y
(x, y)
6) ____________________
7) _______________________
8) _______________________
______________________
_________________________
__________________________
______________________
_________________________
__________________________
For problems 9 and 10, you have to recall how to solve problems using absolute value | |.
* 10) y = ‒|𝑥|
*9) y = |𝑥|
x
y
(x, y)
x
y
(x, y)
9) _____________________
10) _____________________
_______________________
________________________
_______________________
________________________