Understanding the Slope of a Horizontal Line Through Points 10-7 and 5-7
Introduction
The mathematical concept of slope is fundamental to understanding various geometric properties of lines. This article delves into the calculation of the slope for a specific line, which passes through the points (10, -7) and (5, -7). By understanding this, we can explore the properties of horizontal lines and their relevance in geometry and real-world applications.
What is the Slope of the Line that Passes Through 10-7 and 5-7?
To find the slope of a line that passes through the points (10, -7) and (5, -7), we use the slope formula:
slope (m) ( frac{y_2 - y_1}{x_2 - x_1} )
Here, the coordinates (x_1, y_1) are (10, -7) and (x_2, y_2) are (5, -7).
Calculating the Slope Using the Slope Formula
Substituting the given values into the formula, we proceed as follows:
m ( frac{-7 - (-7)}{5 - 10} )
( frac{-7 7}{5 - 10} )
( frac{0}{-5} )
0
Thus, the slope of the line is 0. This means the line is horizontal and parallel to the x-axis. The equation of this line can be written as y -7.
Alternative Approach to Understanding the Slope
Another way to visualize this is through the change in y and x values. The formula for slope is:
slope (m) ( frac{Delta y}{Delta x} ) ( frac{y_2 - y_1}{x_2 - x_1} )
Applying the data for points (10, -7) and (5, -7):
( frac{-7 - (-7)}{5 - 10} ) ( frac{-7 7}{5 - 10} ) ( frac{0}{-5} ) 0
As the y-values are the same, the line is parallel to the x-axis.
Conclusion
In summary, the slope of the line that passes through the points (10, -7) and (5, -7) is 0, indicating a horizontal line. This line is parallel to the x-axis and the equation stating this is y -7. Understanding the slope, particularly for horizontal lines, is crucial in various applications in mathematics and beyond.