Question

Draw and label a coordinate plane on a piece of grid paper. Then graph and label each point. \(N(1,-5)\)

Short answer

Plot point N(1,-5) by moving 1 unit right and 5 units down from the origin.

Step-by-step solution

Prepare the Coordinate Plane

Take a piece of grid paper and draw two perpendicular lines intersecting at the center of the paper. Label the horizontal line as the 'x-axis' and the vertical line as the 'y-axis'. Mark the intersection point as the origin, denoted as \(O(0,0)\).

Choose the Scale

Decide on a scale for each axis. For this exercise, let's use one grid square to represent one unit on both the x-axis and the y-axis. Mark integers on each axis, extending equally in both positive and negative directions.

Locate the Point N(1,-5)

Start at the origin \(O(0,0)\). Move 1 unit to the right along the x-axis since the x-coordinate of point N is 1. Then, from that point, move 5 units down parallel to the y-axis because the y-coordinate is -5.

Plot and Label the Point

Where your movement on the grid ends, place a dot to represent point N. Label this point as \(N(1,-5)\). Make sure it's clear and distinct on the grid.

Key concepts

Graphing Points

When it comes to math, graphing points is a fundamental skill. It allows us to visualize numbers and their relationships on a grid. A point is a specific location on this grid plane, identified by an ordered pair of numbers called coordinates. Each point tells us exactly where to move on the grid to find it.

To graph a point, follow these steps:

• Identify the coordinates, which are typically in the form \( (x, y) \), where \( x \) is the position on the x-axis and \( y \) is the position on the y-axis.
• Start at the origin, which is the center point of the coordinate plane, labeled as \( O(0,0) \) and marked where the x-axis and y-axis intersect.
• Move along the x-axis by the amount indicated by the x-coordinate.
• Then, move along the y-axis by the amount indicated by the y-coordinate.

By practicing these steps, you'll be able to quickly and accurately pinpoint locations on a graph.

x-axis and y-axis

The coordinate plane is seamlessly divided by two axes: the x-axis and the y-axis. Understanding these axes is essential for graphing points and interpreting graphs.

The x-axis is a horizontal line that runs left to right. The positive numbers extend to the right of the origin, while the negative numbers stretch to the left. It's like a number line laid flat along the horizontal path.

The y-axis is a vertical line that runs up and down. Above the origin, you'll find positive numbers; below the origin, negative numbers are represented.

• The intersection of these two lines at the origin \( O(0,0) \) is what separates the plane into four quadrants.
• These quadrants help us to label and categorize different sections of our graph.
• Each point's coordinates are determined by how far they stand from the origin along these axes.

Once you master the x-axis and y-axis, you'll be able to plot points and draw graphs with ease!

Plotting Coordinates

Plotting coordinates involves taking the identified x and y values from a pair of coordinates and using them to position a point on the coordinate plane. It's a way of translating numeric information into a visual form to make it easier to understand.

Here's how you do it:

• First, examine your coordinate pair. For instance, \( N(1, -5) \). This means you'll start from the origin and move according to these two numbers.
• Move to the right 1 unit along the x-axis, because the x-coordinate is 1.
• Next, from that new position, move downward 5 units since the y-coordinate is -5 (note the downward direction due to the negative sign).
• Place a dot at the endpoint of your movement to denote the point.
• Label the dot with its coordinate name, in this case, \( N(1, -5) \), to identify it clearly.

With practice, plotting coordinates becomes second nature, allowing you to effortlessly interpret and represent data on a graph.