Graph each equation in a rectangular coordinate system. y = -2

Verified step by step guidance

1. Identify the type of equation given. The equation \(y = -2\) represents a horizontal line because \(y\) is constant for all values of \(x\).
2. Understand that for any value of \(x\), the value of \(y\) will always be \(-2\). This means the line is parallel to the \(x\)-axis.
3. To graph the line, plot several points where \(y = -2\). For example, points like \((0, -2)\), \((1, -2)\), and \((-1, -2)\) all lie on the line.
4. Draw a straight horizontal line through all these points extending across the coordinate plane.
5. Label the line with its equation \(y = -2\) to clearly indicate which line you have graphed.

Key Concepts

Graphing Horizontal Lines

A horizontal line in the coordinate plane has the same y-value for all x-values. The equation y = -2 represents a horizontal line crossing the y-axis at -2, meaning every point on the line has y-coordinate -2 regardless of x.

Rectangular Coordinate System

The rectangular coordinate system consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Points are located using ordered pairs (x, y), where x is the horizontal position and y is the vertical position.

Plotting Points from an Equation

To graph an equation, identify points that satisfy it by substituting values for variables. For y = -2, choose any x-values and plot points with y fixed at -2, then connect these points to form the line.