How to Find the Slope Between Two Points: A Step-by-Step Guide
Quick Answer
To find the slope between two points, use the formula m = (y2 - y1) / (x2 - x1). For the points (-14, -13) and (30, 74), the slope is 87/44.
Finding the slope of a line that passes through two points is a fundamental concept in algebra and is crucial for understanding linear relationships. The slope (often represented as 'm') indicates how steep a line is and the direction it travels.
To calculate the slope, we use the formula:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
Where:
- (x1, y1) is the first point, and
- (x2, y2) is the second point.
### Example Calculation
Let’s apply this formula to the points (-14, -13) and (30, 74). Here, we assign:
- x1 = -14,
- y1 = -13,
- x2 = 30,
- y2 = 74.
Now, we can substitute these values into the slope formula:
$$ m = \frac{74 - (-13)}{30 - (-14)} $$
This simplifies to:
$$ m = \frac{74 + 13}{30 + 14} = \frac{87}{44} $$
This fraction represents the slope of the line. Since 87 and 44 share no common factors other than 1, we can conclude that this is the simplified form of the slope.
### Understanding the Slope
The slope of $$ \frac{87}{44} $$ tells us that for every 87 units the line rises vertically, it moves 44 units horizontally to the right. A positive slope indicates that the line rises as you move from left to right, suggesting a positive relationship between the x and y values. This concept is widely applicable, including in fields such as physics, economics, and statistics, where relationships between variables are analyzed.
### Real-World Application
Understanding slope is essential for various real-world scenarios. For instance, in architecture, the slope of a roof is crucial for ensuring proper drainage. In economics, the slope of a demand curve can indicate how the quantity demanded changes with price fluctuations.
### Conclusion
Mastering how to find the slope between two points will empower you with the skills to analyze relationships in different contexts. Keep practicing with different sets of points to strengthen your understanding. If you want more examples or a deeper dive into equations, check out the equations section on Train Your Brain!
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