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Chapter 5: Problem 2

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

Short Answer

Expert verified
Plot (3, -1) by moving 3 units right and 1 unit down from the origin.

Step by step solution

01

Understand the coordinate system

Recall that the coordinate system consists of two perpendicular lines called axes. The horizontal axis is known as the x-axis, and the vertical axis is the y-axis. The point where these axes intersect is called the origin, denoted as (0,0). Each point in this system is represented as an ordered pair (x,y), where x indicates horizontal position, and y indicates vertical position.
02

Identify the coordinates

For the given point (3, -1), the first number 3 is the x-coordinate, which tells you the position along the x-axis. The second number -1 is the y-coordinate, which tells you the position along the y-axis.
03

Plot the x-coordinate

Start at the origin (0,0). Move 3 units to the right along the x-axis because the x-coordinate is positive.
04

Plot the y-coordinate

From the point (3,0) where you ended in Step 3, move 1 unit down because the y-coordinate is -1.
05

Mark the point

The new location you arrive at after moving 3 units right and 1 unit down is the point (3,-1). Put a dot at this location to represent the point.

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Key Concepts

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

Coordinate System
The foundation of graphing points starts with understanding the coordinate system. This system is composed of two intersecting lines known as axes. The horizontal line is the x-axis, and the vertical line is the y-axis. They meet at the origin, which is labeled as (0,0). Each position on this system is marked by an ordered pair, called coordinates, written as (x,y). The coordinate system is essential for visualizing and locating points in any plane. Knowing what each component represents helps in plotting points correctly and understanding spatial relationships.
x-axis and y-axis
The x-axis and y-axis are the basic building blocks of the coordinate system.

The x-axis runs horizontally, and values increase as you move right from the origin. Conversely, they become negative as you move left. The y-axis runs vertically where values increase as you go up and decrease as you go down from the origin.

For example, if a coordinate is given as (3, -1), then the x-coordinate, which is 3, tells us to move three units to the right along the x-axis. The y-coordinate, which is -1, instructs us to move one unit down along the y-axis.

Knowing how to interpret these axes allows you to accurately pinpoint any position within the coordinate plane.
Plotting Points on Graph
Plotting points on a graph may seem complex, but it becomes straightforward once you understand the process.

First, start at the origin, (0,0). For the given point (3, -1), identify the two components: 3 (the x-coordinate) and -1 (the y-coordinate). Begin by moving 3 units to the right because the x-coordinate is positive. This positions you at (3,0). Now, from this new position, move 1 unit down since the y-coordinate is -1. You are now at the point (3,-1).

Finally, mark the point on the graph. By repeating these steps, you can plot any point with ease and accuracy.

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Most popular questions from this chapter

b. Find the equation of the line through each pair of points. $$ (1,1) \text { and }(3,0) $$

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Change each of the following equations to slope-intercept form, and find the slope. $$ 5 x-y+2=0 $$

Change each of the following equations to slope-intercept form, and find the slope. $$ -6=6 x+6 y $$

For each of the following, find the slope of the line through the given points. $$ (-1,-4) \text { and }(-2,-4) $$
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