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Chapter 5: Problem 5

For each of the following, graph the given points. $$ (0,3) $$

Short Answer

Expert verified
Plot (0,3) by moving 3 units up from the origin.

Step by step solution

01

- Understand the Coordinate System

The coordinate system consists of two axes: the horizontal axis (x-axis) and the vertical axis (y-axis). Points are given in the format (x, y), where x is the position on the horizontal axis and y is the position on the vertical axis.
02

- Identify the Coordinates

Identify the x and y coordinates from the given point (0, 3). Here, x = 0 and y = 3.
03

- Plot the x-coordinate

Move along the x-axis to the x-coordinate value. In this case, the x-coordinate is 0, so stay at the origin (where the x-axis and y-axis intersect).
04

- Plot the y-coordinate

From the x-axis (the origin point here), move vertically to the y-coordinate value, which is 3. Count 3 units up along the y-axis.
05

- Mark the Point

Mark the point where the x and y coordinates intersect. This is the point (0, 3) on the graph.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Coordinate System
A coordinate system helps us locate points on a plane using two number lines. These number lines are known as axes. The horizontal line is called the x-axis, and the vertical line is the y-axis. Both axes cross at a point named the origin, marked as (0, 0). Points on this system are given as pairs (x, y), where:
  • x represents the position along the x-axis.
  • y represents the position along the y-axis.
Using this system, we can precisely determine the location of any point on the plane.
The X-Axis
The x-axis runs horizontally across the coordinate plane. It is the baseline from which we measure horizontal distances.
  • Positive x-values are located to the right of the origin.
  • Negative x-values are located to the left of the origin.
For instance, if you have a point (3, 0), you would move 3 units to the right along the x-axis. If the x-value was -3, you would move 3 units to the left. Understanding how to navigate the x-axis is crucial for plotting points correctly.
The Y-Axis
The y-axis runs vertically on the coordinate plane. It is used to measure vertical distances from the origin.
  • Positive y-values are above the origin.
  • Negative y-values are below the origin.
If you have a point (0, 3), you start at the origin and move 3 units up. If the point was (0, -3), you would move 3 units down. Remembering how to move along the y-axis helps in precisely locating points.
Plotting Points
When plotting points, we use both the x and y coordinates to find the exact spot on the coordinate plane. Here鈥檚 a step-by-step guide:
  • Identify the x and y coordinates from the point. For example, with the point (0, 3), x = 0 and y = 3.
  • Start at the origin, where the x-axis and y-axis meet (0, 0).
  • Move horizontally to the x-coordinate. In this case, stay at 0 on the x-axis.
  • From this point on the x-axis, move vertically to the y-coordinate. Here, move 3 units up.
  • Mark this point on the graph. You have now plotted the point (0, 3).
By following these steps, you can plot any point accurately on the coordinate plane.

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