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Chapter 3: Problem 49

Graph each linear equation. \(x+2=0\)

Short Answer

Expert verified
Draw a vertical line at x = -2.

Step by step solution

01

Rewrite the Equation

Start by analyzing the given equation. We have:\[ x + 2 = 0 \]Subtract 2 from both sides to isolate x:\[ x = -2 \]
02

Understand the Equation

The equation \( x = -2 \) is a vertical line. It means that for any value of y, x will always be -2.
03

Draw the Vertical Line

On the coordinate plane, find the point where x equals -2. A vertical line should be drawn at x = -2 that extends infinitely in both the positive and negative y-directions.
04

Label the Graph

Ensure to label the vertical line as \( x = -2 \) to clearly communicate the graphed equation.

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Key Concepts

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

vertical lines
A vertical line is one of the simplest types of lines to understand in math. It looks like a straight up-and-down line on the graph. Every point on this line has the same x-value. For example, if you have the equation \( x = -2 \), it means all the points on the line have an x-coordinate of -2. The y-values can be anything, whether positive, negative, or zero. This makes the vertical line consistent and easy to draw as it only depends on a single x-value.
isolation of variables
Isolating a variable means getting one variable alone on one side of the equation. This is a crucial step in solving equations. Let's look at our example: \ \[ x + 2 = 0 \],\ To isolate \( x \), you need to perform operations that leave \( x \) alone. Here, we subtract 2 from both sides of the equation: \ \[ x = -2 \].\ This step helps in understanding the exact requirement in graphing or solving further.
coordinate plane
The coordinate plane is a two-dimensional space where we can plot points, lines, and curves. It has two axes: the horizontal x-axis and the vertical y-axis. Each point on the plane is identified by an ordered pair \( (x, y) \). In our example, to draw the line \( x = -2 \), we find \( x = -2 \) on the x-axis and draw a vertical line through it. This visual tool helps us easily interpret and represent mathematical equations and their solutions.
labeling graphs
Labeling graphs is essential for clarity and communication. After you have drawn your graphs, you should label them correctly so anyone looking can understand what they represent. For instance, in our exercise, once we draw the vertical line at \( x = -2 \), we should write \( x = -2 \) next to the line to indicate what the line represents. Proper labeling ensures that both you and others can easily read and understand your graph without confusion.

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Most popular questions from this chapter

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 3 x=9 y $$

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ 3 y=-6 $$

Graph each linear equation. \(-3 x+y=-6\)

Describe what the graph of each linear equation will look like in the coordinate plane. (Hint: Rewrite the equation if necessary so that it is in a more recognizable form.) $$ x+4=3 $$

Solve each problem. The height \(y\) (in centimeters) of a woman is related to the length of her radius bone \(x\) (from the wrist to the elbow) and is approximated by the linear equation $$ y=3.9 x+73.5 $$ (a) Use the equation to approximate the heights of women with radius bone of lengths \(20 \mathrm{cm}, 26 \mathrm{cm},\) and \(22 \mathrm{cm} .\) (b) Write the information from part (a) as three ordered pairs. (c) Graph the equation, using the data from part (b). (d) Use the graph to estimate the length of the radius bone in a woman who is \(167 \mathrm{cm}\) tall. Then use the equation to find the length of the radius bone to the nearest centimeter.
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