Pregunta
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For the following equation, complete the given ordered pairs. Then use any two of the ordered pairs to graph the solution set for the equation. \( x=5 \) \( \left(\begin{array}{l}-3 \\ (0) \\ , 1)\end{array}\right. \)

Ask by Vega Kelley. in the United States
Mar 20,2025

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The equation \( x = 5 \) means all points have an \( x \)-coordinate of 5. The ordered pairs are \((5, -3)\), \((5, 0)\), and \((5, 1)\). To graph, plot these points and draw a vertical line through them.

Solución

1. The equation is \[ x=5. \] This means that the \(x\)-coordinate of every solution must be \(5\), regardless of the value of \(y\). 2. Given the incomplete ordered pairs \[ \left(\begin{array}{l} -3 \\ (0) \\ ,\ 1 \end{array}\right. \] we interpret these as the \(y\)-coordinates that need to be paired with \(x=5\). Thus, the completed ordered pairs are: - \(\left(5,\ -3\right)\) - \(\left(5,\ 0\right)\) - \(\left(5,\ 1\right)\) 3. To graph the solution set, we only need two points. For example, choose: - \(\left(5,\ -3\right)\) - \(\left(5,\ 1\right)\) 4. Plot these points on the coordinate plane: - \(\left(5,\ -3\right)\) is at \(x=5\) and \(y=-3\). - \(\left(5,\ 1\right)\) is at \(x=5\) and \(y=1\). 5. Draw a vertical line through these points. Since every point on this vertical line has \(x=5\), the line represents the solution set of the equation \(x=5\).

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Mind Expander

To complete the ordered pairs for the equation \( x = 5 \), we can choose any \( y \) values we like because this equation is vertical, meaning it has the same \( x \) value regardless of what \( y \) is. Thus, your completed ordered pairs can be: 1. \( (-3, 5) \) 2. \( (0, 5) \) 3. \( (1, 5) \) Next, you can choose any two of these pairs to graph the solution set. For example, if you select \( (0, 5) \) and \( (1, 5) \), you will plot these points on the Cartesian plane, and you will see that a vertical line can be drawn through these points at \( x = 5 \), indicating all points where \( x \) is equal to 5. Happy graphing!

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