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Chapter 11: Problem 66

In the following exercises, graph by plotting points. $$ x+y=-2 $$

Short Answer

Expert verified
Rewrite as \(y = -x - 2\), plot points (0, -2), (1, -3), (-1, -1), and draw the line through them.

Step by step solution

01

Rewrite the equation in slope-intercept form

First, rewrite the given equation \(x + y = -2\) in the slope-intercept form \(y = mx + b\). Subtract \(x\) from both sides: \(y = -x - 2\). This will help identify the slope and intercept for graphing.
02

Identify key points

Choose values of \(x\) to find corresponding values of \(y\). For example, if \(x = 0\), then \(y = -2\).Let's create a table for more values:\[\begin{array}{|c|c|}\hlinex & y \ \hline0 & -2 \ 1 & -3 \ -1 & -1 \ \hline\end{array}\]
03

Plot the points

Plot the points (0, -2), (1, -3), and (-1, -1) on the coordinate plane. Ensure each point is correctly marked according to the values obtained in the table.
04

Draw the line

Draw a straight line through the plotted points. This line represents the graph of the equation \(x + y = -2\). Ensure the line extends across the graph to show the direction of the equation.

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Key Concepts

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

slope-intercept form
The first step in graphing a linear equation is to convert it into the slope-intercept form. The slope-intercept form of a linear equation is written as: \ \(y = mx + b\). Here, \ \(m\) represents the slope of the line, and \ \(b\) represents the y-intercept. The y-intercept is the point where the line crosses the y-axis.
plotting points
Once the equation is in slope-intercept form, the next step is to plot points on the coordinate plane. To do this, we select values for \ \(x\) and use the equation to find the corresponding \ \(y\) values. This gives us coordinates that we can plot.
coordinate plane
The coordinate plane is a two-dimensional surface where we can graph the points and lines that represent equations. It is defined by two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in the plane is identified by an ordered pair \ \((x, y)\).

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Most popular questions from this chapter

In the following exercises, graph each equation. $$ y=x $$

In the following exercises, graph by plotting points. $$ 3 x+y=7 $$

In the following exercises, find the slope of each line. $$ y=2 $$

In the following exercises, identify the most convenient method to graph each line. $$ y=-3 $$

In the following exercises, use the slope formula to find the slope of the line between each pair of points. $$ (3,5),(4,-1) $$
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