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

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Identify the type of equation given. The equation \(y = -2\) represents a horizontal line because \(y\) is constant for all values of \(x\).

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.

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.

Draw a straight horizontal line through all these points extending across the coordinate plane.

Label the line with its equation \(y = -2\) to clearly indicate which line you have graphed.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.