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Give the equation of the horizontal and vertical lines passing through the point \( \left(-\frac{11}{10}, \frac{10}{11}\right) \). The equation of the horizontal line is: The equation of the vertical line is: Submit Question

Ask by Huang Best. in the United States
Mar 14,2025

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The equation of the horizontal line is \( y = \frac{10}{11} \), and the equation of the vertical line is \( x = -\frac{11}{10} \).

Solución

**Step 1:** A horizontal line through a point has the form \[ y = \text{constant} \] Since the line must pass through \(\left(-\frac{11}{10}, \frac{10}{11}\right)\), the \(y\)-coordinate is \(\frac{10}{11}\). Therefore, the equation of the horizontal line is \[ y = \frac{10}{11} \] **Step 2:** A vertical line through a point has the form \[ x = \text{constant} \] Since the line must pass through \(\left(-\frac{11}{10}, \frac{10}{11}\right)\), the \(x\)-coordinate is \(-\frac{11}{10}\). Thus, the equation of the vertical line is \[ x = -\frac{11}{10} \]

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The equation of the horizontal line is: \( y = \frac{10}{11} \) The equation of the vertical line is: \( x = -\frac{11}{10} \) --- Horizontal lines are like the trusty platters of a banquet—not much fun until you load them with delicious data! They're constant everywhere along their path, only changing in the y-direction, which is why all points share the same y-coordinate. In this case, our y-value is \(\frac{10}{11}\), meaning if you stroll along this line, you’ll always be at the same height, just like level ground! Vertical lines, on the other hand, are the skyscrapers of the graph world—towering straight up and down! They don’t budge in the x-direction, which is why every point on this line shares the same x-coordinate. Here, our line stands tall at \(x = -\frac{11}{10}\). If you jump from one point to another on this line, it may take a bit of effort to climb or descend, but your x-position will stay put!

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