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A linear equation is an equation that forms a straight line when plotted on a graph. To solve a linear equation, you need to find the values of the variables that make the equation true. Let's consider the equation given: \(2x + y = -8\). This equation shows how the variables \(x\) and \(y\) relate to each other.

To solve for \(y\) when \(x = 0\), you substitute \(0\) for \(x\) in the equation: \(2(0) + y = -8\). This simplifies to \(y = -8\).

Next, to solve for \(x\) when \(y = 0\), substitute \(0\) for \(y\) in the equation: \(2x + 0 = -8\), which simplifies to \(2x = -8\). Dividing both sides by 2, we get \(x = -4\).

Lastly, to solve for \(y\) when \(x = 3\), substitute \(3\) for \(x\) in the equation: \(2(3) + y = -8\), which simplifies to \(6 + y = -8\). Subtracting 6 from both sides, we get \(y = -14\).

• When \(x = 0\), \(y = -8\)
• When \(y = 0\), \(x = -4\)
• When \(x = 3\), \(y = -14\)

Graphing solutions of a linear equation involves plotting points on the coordinate plane that satisfy the equation and then drawing a line through these points.

For the given equation \(2x + y = -8\), we have identified three solutions: \( (0, -8) \), \( (-4, 0) \), and \( (3, -14) \). To graph these solutions:

• First, place the point \( (0, -8) \) on the graph. This point is found where \( x = 0 \) and \( y = -8 \).
  
• Next, place the point \( (-4, 0) \) on the graph. This is where \( x = -4 \) and \( y = 0 \).


• Finally, place the point \( (3, -14) \) on the graph. This point corresponds to \( x = 3 \) and \( y = -14 \).

After plotting these points, draw a straight line through them, representing the graph of the equation \(2x + y = -8 \). This line shows all possible solutions of the equation on the coordinate plane.

The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. It consists of two perpendicular lines: the horizontal axis (x-axis) and the vertical axis (y-axis). The point where these axes intersect is called the origin, labeled \( (0,0) \).

Each point on the coordinate plane is determined by an \(x\)-value and a \(y\)-value, written as an ordered pair \( (x, y) \). The x-value tells you how far to move left or right from the origin, while the y-value tells you how far to move up or down.

For example, the point \( (-4, 0) \) means you move 4 units to the left along the x-axis and stay on the y-axis since the y-value is 0.

In our equation \(2x + y = -8\), plotting points \( (0, -8) \), \( (-4, 0) \), and \( (3, -14) \) on the coordinate plane helps visualize the relationship between \(x\) and \(y\). Drawing straight lines through these points helps illustrate how the solutions form a linear path across the plane.