Question

Draw and label a coordinate plane on a piece of grid paper. Then graph and label each point. \(M(-6,-2)\)

Short answer

Draw the axes, label points, locate (-6,-2), plot and label as M.

Step-by-step solution

Draw the Coordinate Plane

Start by drawing the coordinate plane on your grid paper. This includes the x-axis (horizontal line) and y-axis (vertical line). Ensure that both axes intersect at the origin point (0,0) and extend in both positive and negative directions.

Label the Axes

Label the x-axis with positive numbers increasing to the right and negative numbers increasing to the left. Similarly, label the y-axis with positive numbers increasing upwards and negative numbers increasing downwards. Mark each unit on the grid clearly for accurate graphing.

Locate Point M(-6,-2)

Start from the origin (0,0) and move 6 units to the left on the x-axis to locate the x-coordinate -6. Then, from this point, move 2 units downwards to find the y-coordinate -2.

Plot and Label the Point

Mark the point where your movements along the x-axis and y-axis meet. This is point M(-6,-2). Clearly label this point on the grid by writing 'M' next to the dot you plotted.

Key concepts

Graphing Points

Graphing points on a coordinate plane can be an easier task when you break down the steps. Once you understand the basics, it’s like plotting a treasure map where every point tells a story. A "point" in this context is essentially an exact location on the plane that is defined by two numbers.
• The numbers come in pairs, known as coordinates, consisting of an x-coordinate (the first number) and a y-coordinate (the second number).
• Points are often labeled, like point M in our exercise, and are enclosed in parentheses, for example, \((-6, -2)\).
When graphing such a point, you always start at the origin, which is \((0, 0)\), where the x-axis and y-axis intersect. From the origin, you:

• Move left or right to match the x-coordinate, depending on if it's a negative or positive number.
• Move up or down to correspond to the y-coordinate.

Ultimately, visualizing where these paths intersect assists in accurately plotting your point on the graph.

x-axis and y-axis

The x-axis and y-axis are the basic building blocks of a coordinate plane, and understanding them is essential for graphing any point. Let's take a closer look at what each axis represents:
The **x-axis** is the horizontal line that stretches across your graph. It is crucial for determining the horizontal position of any point.

• The right side of the x-axis represents positive numbers.
• The left side displays negative numbers.

It's important to note that the numbering is usually in equal increments and moves away from the origin.
The **y-axis**, on the other hand, stands as the vertical line, providing essential information about vertical placement.

• Numbers above the origin are positive.
• Numbers below are negative.

Both axes meet at the origin, \((0, 0)\), and it's from here that you start plotting points like we did for \(M(-6, -2)\), moving along these axes to find the correct location.

Grid Paper

Grid paper is a helpful tool when working with graphs as it automatically guides the way you plot points.
The paper is divided into small, uniform squares that make it easier to keep your notes neat and your measurements accurate.
With grid paper, you have a visible grid that:

• Assists with visual spacing, ensuring each step is precise when moving along the axes.
• Makes labeling and reading coordinates straightforward, since each square represents a unit.
• Helps in keeping all movements confined within distinct lines, which is especially beneficial when teaching or working with detailed graphs.

Using grid paper as your backdrop not only enhances your ability to plot accurately but also helps in easily identifying mistakes, making corrections much simpler. It's essentially your best friend while mastering the coordinate plane.