Generating Patterns and Graphing Relationships

Consider the table given below.

 

 

Let's find the relationship between x and y.

 

Observe that:

Row 1: 1 + 2 = 3

Row 2: 2 + 2 = 4

Row 3: 3 + 2 = 5

Row 4: 4 + 2 = 6

 

So, x + 2 = y.

 

The rule or the function is y = x + 2.

 

Now, let's find the ordered pairs and draw the graph.

 

Each row in the table represents an ordered pair.

An ordered pair (x, y) tells the location of a point on the coordinate plane.

The x-coordinate (x-value) tells the distance of the point from the origin in the horizontal direction. The y-coordinate (y-value) tells the distance of the point from the origin in the vertical direction.

 

The ordered pairs for the given x- and y-values are (1, 3), (2, 4), (3, 5), and (4, 6).

 

Now, plot a point for each ordered pair.

First plot the point (1, 3). Start at (0, 0) and move 1 unit right and 3 units up.

Similarly, plot the other points.

Then, draw a line passing through these points. The line represents all ordered pairs that follow the rule.