Graphing Basics

Graphing Basics

Intro to the coordinate plane

Remember the number line?

You probably used this before. The numbers you use can be placed on this line. the number 1 would go over the number 1 on the number line. numbers less than 0, called negative numbers were introduced later, but they still had a place on the number line. A number line is a one dimensional representation of a way to express numbers. What if we wanted a two dimensional representation.

Now we have two number lines.

The original number line still goes left and right, but the new number line goes up and down. Now we have a two dimensional representation. The two number lines combined are called a coordinate plane. We can not only put numbers on our number lines, but also to the left, right, up, and down of the number lines.

A coordinate plane has labels to help us navigate.

Quadrants are the 4 areas created when we combined the number lines. The top right is Quadrant 1 and we move counterclockwise(the opposite way a clock moves) towards quadrant 2, 3 and 4. We also want to label the number lines. We call the original number line the X-axis and the other number line the Y-axis. got it?

Multiple Choice

The EMS is in what Quadrant?

• 1

• 2

• 3

• 4

Multiple Choice

The FIRE is in what quadrant?

• 1

• 2

• 3

• 4

Multiple Choice

the X-axis goes?

• up and down

• right

• left and right

• up

Multiple Choice

The Y-axis goes

• up

• right

• up and down

• left and right

If we have two number lines, we will have two numbers.

Since the X-axis represents the original number line, we will list that number first. The Y-axis number, will be listed second. We want to separate the two numbers with a comma and put parenthesis around them, so we know we are referencing numbers in our coordinate plane: (X,Y).

(X,Y) is used to represent our two numbers.

X represents the value from the center of the left and right number line and Y represents the value from the center of the up and down number line. The center of both number lines is the value 0. So we can represent the center of both number lines in our coordinate plane as (0,0), called the origin point.

To find any point on our coordinate plane...

we need to know the two numbers. We know the first number will represent our left and right value on the X-axis. We know our second number will represent the up and down value on the Y-axis. Our X-axis number is at 3 and our Y-axis number is at 4. They intersect at that dot seen in our picture, we would label that dot as (3,4).

Think of a coordinate system as an empty classroom.

Where would you place the desks and chairs? The X-axis and Y-axis are used to help give us coordinates on where things are placed. Notice in the picture how we labeled the various points. Our first number the distance left and right, and our second number the distance up and down from the origin point; (x,y).

try labeling some yourself.

Multiple Choice

What would you label point C?

• (-1 , 3)

• (3, -1)

• (1, 3)

• (3, 1)

Multiple Choice

What would you label point E?

• (-3, 3)

• (3, -3)

• (-3, -3)

• (3, 3)

Did you get points C and E correct?

Point C is has a value of negative 1 on the X-axis and it has a value of positive 3 on the Y-axis; (-1, 3)

Point E has a value of positive 3 on the X-axis and it has a value of negative 3 on the Y-axis; (3, -3).

Remember always list the X value first as it represented the original number line, then list the Y value next; (X,Y)

Sometimes a value can equal zero.

Notice the coordinates(points)

(5, 0) and (0, -3) on this graph.

(5,0) had us move 5 units right, but we did not move up or down at all. (0, -3) had us move down to -3, but we did not move left or right at all. Our points can be anywhere on our graph, we just need to label them correctly.