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Find the equation of the line through the points \( (4,-5) \) and \( (9,-5) \).

Ask by Harmon Perkins. in the United States
Mar 10,2025

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Answer

The equation of the line is \( y = -5 \).

Solution

1. Calculate the slope \( m \): \[ m = \frac{y_2-y_1}{x_2-x_1} = \frac{-5 - (-5)}{9-4} = \frac{0}{5} = 0. \] 2. Since the slope is 0, the line is horizontal. The equation of a horizontal line through \( y = -5 \) is: \[ y = -5. \] Thus, the equation of the line is \( y = -5 \).

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Beyond the Answer

The points \( (4, -5) \) and \( (9, -5) \) show that both points have the same y-coordinate, which indicates that this is a horizontal line. The equation for a horizontal line is of the form \( y = c \), where \( c \) is the y-coordinate of any point on the line. Thus, the equation of the line through these points is \( y = -5 \). Interestingly, horizontal lines are a special case in geometry. They remind us that sometimes, things can be simpler than they seem—like navigating life’s challenges with a steady direction! Furthermore, this concept of lines in a coordinate plane is foundational in algebra and can be seen in various practical situations, like plotting graphs for science experiments or economics. The beauty of math is that it finds its way into the real world!

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