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Chapter 5: Problem 7

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

Short Answer

Expert verified
Plot the point (0,0) at the origin, where the x-axis and y-axis intersect.

Step by step solution

01

Identify the Coordinates

Identify the x-coordinate and y-coordinate of the given point. The point given is \( (0,0) \), where x = 0 and y = 0.
02

Locate the Origin

Since both coordinates are zero, the point \( (0,0) \) is located at the origin of the coordinate plane, which is where the x-axis and y-axis intersect.
03

Plot the Point

Plot the point \( (0,0) \) at the origin on the graph. This is where the horizontal line and vertical line intersect on the graph.

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Key Concepts

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

Coordinate Plane
The coordinate plane is a two-dimensional surface used to plot points, lines, and curves. It is divided into four quadrants by the x-axis (horizontal) and y-axis (vertical). The intersection of these axes is known as the origin. Each point on the plane is represented by an ordered pair \( (x, y) \).
The x-coordinate tells you how far to move left or right from the origin. The y-coordinate tells you how far to move up or down.
Here's a quick reference to help visualize the coordinate plane:
  • First Quadrant: x > 0 and y > 0
  • Second Quadrant: x < 0 and y > 0
  • Third Quadrant: x < 0 and y < 0
  • Fourth Quadrant: x > 0 and y < 0
Plotting Points
Plotting points on the coordinate plane involves identifying the x and y coordinates and marking that spot.
For example, to plot the point \( (0,0) \), follow these steps:
  • Find the x-coordinate (0) on the x-axis.
  • Find the y-coordinate (0) on the y-axis.
  • Draw a dot where the x and y values intersect, which is the origin in this case.
Plotting different coordinates allows us to create shapes, lines, and curves, unlocking many possibilities in geometry and algebra.
Keep practicing with different points to become more comfortable with the process!
Origin
The origin is the point where the x-axis and y-axis intersect, marked as \( (0,0) \). It is the starting point for locating all other points on the coordinate plane.
When plotting points, the origin acts as a reference. If a point has an x-coordinate of 0 and a y-coordinate of 0, it lies directly at the origin.
Understanding the origin is essential in graphing because it helps you orient yourself on the plane and better understand the relationships between different points.
Try plotting different points from the origin to see how they relate to each other and get a feel for the layout of the coordinate plane.

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Most popular questions from this chapter

What are the slope and the y-intercept of each of these lines? Graph the lines using the slope-intercept method. $$ 2 x+6 y=16 $$

For each of the following, graph the given points. $$ (3,-1) $$

b. Find the equation of the line through each pair of points. $$ (0,4) \text { and }(2,0) $$

For each of the following, find the slope of the line through the given points. $$ (5,0) \text { and }(0,2) $$

Graph each of the following inequalities. $$ y<2 x-1 $$
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