## Pre-Algebra Tutorial

#### 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

I. (2,0) x-axis
J. (0, 2) y-axis
K. (-2,0) x-axis
L. (0,-2) y-axis
O. (0,0) midpoint 