## Pre-Algebra Tutorial

*Graph Proportional Relationships Part 1- Review*

#### Intro

Graphing proportional relationships is just another way of stating “find the point on the grid or graph.” Coordinates or points can be found on a grid with an x-axis and y-axis, each marked with specific units. The most basic graph below illustrates the key factors of a graph: the x-axis (horizontal), the y-axis (vertical), mid-point (0,0), and the 4 quadrants.

In the second image, you can see examples of how the points on the graph are labeled. The first number inside the parenthesis is always the x-axis and the second is always the y-axis. Notice that the numbers can be negative, which is why we label each quadrant. Quadrant 1- both x and y are positive. Quadrant 2- x is negative, y is positive. Quadrant 3- both x and y are negative. Quadrant 4- x is positive, y is negative. The majority of the graphs we see on a daily basis fall in quadrant 1 because we generally focus on positive relationships. If a point falls on an axis, its value is zero. For example: if a point is 5 on the x-axis and 0 on the y-axis, it would be (5,0).

#### Sample Problem

**Part 1-** Determine which quadrant the coordinates belong in:

1. (1,2)

2. (-3,3)

3. (5,-1)

4. (-2,-2)

5. (0,0)

6. (0,3)

7. (7,0)

**Part 2-** Examine the coordinates and properly label each letter

#### Solution

**Part 1**

1. Quadrant 1- Each point is positive

2. Quadrant 2- X is negative and Y is positive

3. Quadrant 4- X is positive and Y is negative

4. Quadrant 3- Each point is negative

5. None: midpoint- (0,0) is always the middle of the graph and is not in a quadrant

6. None: It is on the y-axis- When the X has no value or is zero, the point will fall on the y-axis and will not be in a quadrant

7. None: It is on the x-axis- When Y has no value or is zero, the point will fall on the x-axis and will not be in a quadrant

**Part 2**

A. (-2,3) Quadrant 2

B. (-3, 2) Quadrant 2

C. (-3,-2) Quadrant 3

D. (-2,-3) Quadrant 3

E. (1,-4) Quadrant 4

F. (4, -1) Quadrant 4

G. (4,1) Quadrant 1

H. (1,4) Quadrant 1

I. (2,0) x-axis

J. (0, 2) y-axis

K. (-2,0) x-axis

L. (0,-2) y-axis

O. (0,0) midpoint

# About The Author

Math, Financing, And Accounting |

I am a recent graduate from Kent State University with an Associate of Applied Business and a Bachelor of Business Administration. During my studies, I excelled at math, financing, and accounting and was offered tutoring jobs at the university. Unfortunately, I had to decline the jobs at the time du... |

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