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Vite an equation for the line described. Write the equation in the form specified. \( \begin{array}{llll}\text { 11) parallel to } x=6 \text {, through }(7,2) \\ \begin{array}{llll}\text { A) } x=2 & \text { B) } y=6 & \text { C) } y=2 & \text { D) } x=7\end{array}\end{array} \).

Ask by Maxwell Beck. in Nicaragua
Mar 22,2025

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Tutor-Verified Answer

Answer

La recta paralela a \( x=6 \) que pasa por \( (7,2) \) es \( x=7 \).

Solution

1. La recta \( x=6 \) es una recta vertical. 2. Dos rectas son paralelas si tienen la misma dirección. Por lo tanto, cualquier recta paralela a \( x=6 \) también debe ser vertical. 3. Una recta vertical que pasa por el punto \( (7,2) \) tiene la ecuación \( x=7 \). 4. Comparando con las opciones dadas, la respuesta correcta es la opción D: \( x=7 \).

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Bonus Knowledge

The equation for a vertical line that's parallel to \(x=6\) will also be a vertical line with a specific \(x\)-value. Since the line must go through the point (7, 2), the equation of the line is \(x=7\). So, the correct option is D) \(x=7\). Now, did you know that vertical lines are unique in that they don’t have a slope? Instead, they're thought to have an "undefined" slope since they go straight up and down! This can be quite the mind-bender when you first learn it, but the parallelism helps keep things consistent. Also, this concept of parallel lines isn't just for math! It crops up everywhere, from architecture (think skyscrapers!) to art (parallel brushstrokes can create beautiful patterns). Just as lines remain consistent in their direction, so does the concept of staying true in your pursuits!

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