Question

Draw and label a coordinate plane on a piece of grid paper. Then graph and label each point. \(S(3,6)\)

Short answer

Graph the point S(3,6) on the coordinate plane by moving 3 units right and 6 units up from the origin.

Step-by-step solution

Drawing the Coordinate Plane

On a piece of grid paper, draw two perpendicular lines that intersect. Label the horizontal line as the x-axis and the vertical line as the y-axis. Label the point where they intersect as the origin, point \(O(0,0)\). Mark equal intervals along both the x-axis and the y-axis for consistent scaling. Use the numbers to create a scale for the graph.

Plotting Point S

Locate the point \(S(3,6)\) by first moving 3 units to the right along the x-axis from the origin, as the x-coordinate is 3. From this position, move 6 units up along the y-axis, since the y-coordinate is 6. Mark this spot on the graph.

Labeling Point S

After marking the spot for \(S(3,6)\), label the point with the letter \(S\) at its coordinates to indicate its location on the graph clearly. This helps in visual identification and avoids confusion.

Key concepts

Graphing Points

Graphing points is a fundamental skill in math that allows us to visually represent data on a coordinate plane. A point on the graph is defined by an ordered pair of numbers, which we call coordinates. For example, the point \( S(3,6) \) has an x-coordinate of 3 and a y-coordinate of 6. The ordered pair (x, y) indicates the position of a point on the plane.

To graph a point, you begin by finding its position on the x-axis, and then follow by locating its position on the y-axis. This involves moving horizontally first, then vertically. Graphing is done on a coordinate plane with clear axes and evenly spaced intervals, which ensures accuracy and consistency.

• Horizontal movement is determined by the x-coordinate.
• Vertical movement is determined by the y-coordinate.
• The process of graphing marks the exact location of a point.

X-axis

The x-axis is the horizontal line that runs left to right across the coordinate plane. It serves as a reference line for determining horizontal movement. When graphing points, you always begin at the origin and use the x-coordinate to navigate left or right along this axis.

• Positive x-values move you to the right from the origin.
• Negative x-values move you to the left from the origin.

The x-axis is always labeled and scaled to reflect uniform distances, which helps in easily and accurately locating points. It intersects the y-axis at the origin, forming the baseline of the graph.

Y-axis

The y-axis is the vertical line intersecting the x-axis at the origin. It determines how far you move up or down on the coordinate plane based on the y-coordinate.

Here are some important points about the y-axis:

• Positive y-values move you upward from the x-axis.
• Negative y-values move you downward from the x-axis.

This axis, like the x-axis, is marked at regular intervals to reflect equal spacing. The y-axis is crucial for finding the second part of the coordinate pair after moving along the x-axis. The intersection with the x-axis places the origin at a fixed starting point for graphing.

Origin

The origin is the starting point on a coordinate plane, labeled as point \( O(0,0) \). It is where the x-axis and y-axis intersect, and is the reference point for graphing any point. The coordinates (0,0) represent zero movement along both axes.

The origin provides a crucial point of symmetry on the plane:

• It divides the plane into four quadrants.
• It is always the starting point for graphing any point.
• Coordinate axes are drawn and scaled from the origin.

Understanding the origin is essential, as it helps to accurately locate and plot points by defining the initial position clearly. The origin acts as a center from which movements along the x and y directions are measured.