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Chapter 4: Problem 89

In the following exercises, graph by plotting points. \(2 x+y=-3\)

Short Answer

Expert verified
Plot the points (-2,1), (-1,-1), (0,-3), (1,-5), and (2,-7) and draw a line through them.

Step by step solution

01

Identify the Equation

The given equation is: \[2x + y = -3\]
02

Rearrange for y

Solve the equation for y in terms of x: \[y = -3 - 2x\]
03

Create a Table of Values

Choose different x-values, substitute into the equation, and compute the corresponding y-values.x = -2, y = 1; x = -1, y = -1; x = 0, y = -3; x = 1, y = -5; x = 2, y = -7
04

Plot the Points

Use the table of values to plot the points on a coordinate plane. The points are (-2, 1), (-1, -1), (0, -3), (1, -5), and (2, -7).
05

Draw the Line

Connect the points with a straight line. This line is the graph of the equation \[2x + y = -3\].

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Key Concepts

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

Plotting Points
Plotting points is a fundamental skill in graphing linear equations. When you have a list of coordinates, for instance, (-2, 1), (-1, -1), (0, -3), (1, -5), and (2, -7), you can plot these points on a graph to visualize the equation.
Each point is represented by an (x, y) pair. To plot a point, you start at the origin (0,0) on the graph. Move horizontally according to the x-value and then vertically according to the y-value.
For example, the point (1, -5) means you move 1 unit to the right and 5 units down from the origin. Repeat this process for each point. Remember to label each point to avoid confusion.
Coordinate Plane
The coordinate plane is a two-dimensional space formed by two perpendicular number lines called axes. The horizontal axis is the x-axis, and the vertical one is the y-axis. Where they intersect is called the origin (0,0).
Each point on the plane has a coordinate pair (x, y). Understanding the coordinate plane is crucial, as it allows you to visualize the relationship between x and y in any equation.
For example, in our problem, the relationship is defined by the equation y = -3 -2x, which we can visualize by plotting points. Make sure your axes are properly labeled with positive and negative values and that you scale them appropriately.
Solving for y
To graph a linear equation, it's often helpful to solve for y first. This means rearranging the equation so that y is isolated on one side.
In our example, starting with the equation 2x + y = -3, we solve for y by isolating it:
y = -3 -2x.
By solving for y, substituting x-values to find corresponding y-values becomes straightforward. This step is crucial because it transforms the equation into a form that you can easily use to create a table of values.
Table of Values
A table of values helps you organize the x and y pairs you will plot on the coordinate plane. This table lists different x-values and their corresponding y-values calculated from the equation.
For the equation y = -3 - 2x, we select x-values like -2, -1, 0, 1, and 2. Plugging these values into the equation gives the y-values: 1, -1, -3, -5, and -7, respectively. So, our table looks like this:
  • x = -2, y = 1
  • x = -1, y = -1
  • x = 0, y = -3
  • x = 1, y = -5
  • x = 2, y = -7
Using this table, you can plot each point and draw the line representing the equation.

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