Problem 17
Question
Graph each ordered pair on a coordinate system. $$P(0,6)$$
Step-by-Step Solution
Verified Answer
Plot \(P(0,6)\) on the y-axis 6 units above the origin.
1Step 1: Understand the Ordered Pair
An ordered pair like \(P(0,6)\) consists of two numbers: the first represents the x-coordinate and the second the y-coordinate. This tells us where to position our point on a coordinate plane.
2Step 2: Locate the X-Coordinate
On a coordinate grid, find the vertical line that represents \(x=0\). This line is the y-axis and is where all points with an x-coordinate of 0 are located.
3Step 3: Locate the Y-Coordinate
From the position determined in Step 2, move up the y-axis to \(y=6\). This is the point 6 units above the origin along the vertical axis.
4Step 4: Plot the Point
Mark the point where \(x=0\) and \(y=6\) meet. This is the location of the ordered pair \(P(0,6)\) on the coordinate grid. Label this point as \(P\).
Key Concepts
Understanding the Coordinate SystemUnderstanding the X-CoordinateUnderstanding the Y-CoordinatePlotting Points on a Coordinate System
Understanding the Coordinate System
A coordinate system is a method used for identifying the exact location of points in a plane through a pair of numerical values. In a two-dimensional plane, this system comprises two number lines that intersect at a right angle. The horizontal line is called the x-axis, and the vertical line is referred to as the y-axis. The point where these axes intersect is known as the origin, marked as (0, 0).
In this system, any location is defined by an ordered pair like \(P(0,6)\). Each pair provides us with a clear and precise way to specify positions by giving directions on how far to move along the x-axis and y-axis. This graphical representation helps us visualize data and relationships between different points on a plane. With a coordinate system, we can effectively map out anything from simple points to complex shapes like graphs and lines.
In this system, any location is defined by an ordered pair like \(P(0,6)\). Each pair provides us with a clear and precise way to specify positions by giving directions on how far to move along the x-axis and y-axis. This graphical representation helps us visualize data and relationships between different points on a plane. With a coordinate system, we can effectively map out anything from simple points to complex shapes like graphs and lines.
Understanding the X-Coordinate
The x-coordinate is the first number in an ordered pair, and it specifies a point's location along the x-axis. In our example with the point \(P(0,6)\), the x-coordinate is 0, meaning that the point lies on the y-axis itself.
The x-axis allows us to determine how far left or right a point is from the origin. If the x-coordinate is positive, the point is to the right of the origin, and if it's negative, the point lies to the left. However, when the x-coordinate is 0, like in our case, the point is directly on the y-axis.
The x-axis allows us to determine how far left or right a point is from the origin. If the x-coordinate is positive, the point is to the right of the origin, and if it's negative, the point lies to the left. However, when the x-coordinate is 0, like in our case, the point is directly on the y-axis.
- Determines horizontal position.
- Positive x-values lie to the right.
- Negative x-values lie to the left.
- An x-coordinate of 0 means the point is exactly on the y-axis.
Understanding the Y-Coordinate
The y-coordinate, the second number in an ordered pair, determines how far a point is from the x-axis in a vertical direction. With the ordered pair \(P(0,6)\), our y-coordinate is 6.
By understanding the y-coordinate, you know how high or low the point is relative to the x-axis. If the y-coordinate is positive, the point is above the x-axis. If it's negative, the point is below it. Here, since the y-coordinate is positive 6, it tells us to move straight up 6 units from the x-axis.
By understanding the y-coordinate, you know how high or low the point is relative to the x-axis. If the y-coordinate is positive, the point is above the x-axis. If it's negative, the point is below it. Here, since the y-coordinate is positive 6, it tells us to move straight up 6 units from the x-axis.
- Determines vertical position.
- Positive y-values indicate a position above the x-axis.
- Negative y-values indicate a position below the x-axis.
- A y-coordinate of 6 means moving 6 units up from the x-axis.
Plotting Points on a Coordinate System
To plot a point on a coordinate system, you need to follow a simple process using the coordinates given. Let's take the point \(P(0,6)\) as an example.
First, start by finding the x-coordinate along the x-axis. Since our x-coordinate is 0, you will position yourself at the origin on the y-axis.
Next, look at the y-coordinate. With a y-coordinate of 6, you move up from the x-axis along the y-axis by 6 units. This movement from the origin takes you directly to the point \(P(0,6)\).
First, start by finding the x-coordinate along the x-axis. Since our x-coordinate is 0, you will position yourself at the origin on the y-axis.
Next, look at the y-coordinate. With a y-coordinate of 6, you move up from the x-axis along the y-axis by 6 units. This movement from the origin takes you directly to the point \(P(0,6)\).
- Start with the x-coordinate along the x-axis.
- If x = 0, you begin at the origin on the y-axis.
- Move vertically according to the y-coordinate.
- Plot and label your point at the intersection.
Other exercises in this chapter
Problem 16
Evaluate each expression if \(x=7, y=3,\) and \(z=9\) $$15-2 x$$
View solution Problem 17
Find the value of each expression. $$12 \div 3+21$$
View solution Problem 17
Name the property shown by each statement. $$12 \cdot 8=8 \cdot 12$$
View solution Problem 17
Evaluate each expression if \(x=7, y=3,\) and \(z=9\) $$\frac{6 y}{z}$$
View solution