How to Find the Slope of a Line Between Two Points

Finding the slope of a line is a fundamental concept in algebra that helps us understand how steep a line is and in which direction it goes. The slope is calculated by using the coordinates of two points that the line passes through. Let's break down the process step-by-step.

The formula for finding the slope (m) of a line between two points (x1, y1) and (x2, y2) is given by:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

In your case, the points are (10, 9) and (1, 2). Here, we can assign:
- Point 1: (x1, y1) = (10, 9)
- Point 2: (x2, y2) = (1, 2)

Now, we'll substitute these values into the slope formula:

1. Calculate the change in y (vertical change):
$$y_2 - y_1 = 2 - 9 = -7$$
2. Calculate the change in x (horizontal change):
$$x_2 - x_1 = 1 - 10 = -9$$
3. Now, plug these values into the slope formula:
$$m = \frac{-7}{-9}$$

Since a negative divided by a negative gives a positive result, we simplify this to:
$$m = \frac{7}{9}$$

This means that for every 9 units you move horizontally to the right, the line goes up 7 units.

### Why is Slope Important?
Understanding slope is crucial in various real-life applications. For example, in construction, knowing the slope can help determine the steepness of roofs. In economics, slope can represent the rate of change in cost concerning production levels. In fields such as physics, slope can indicate speed or acceleration when graphed.

### Additional Examples
Let’s solidify your understanding with a couple more examples:
1. For the points (4, 5) and (1, 1):
$$m = \frac{1 - 5}{1 - 4} = \frac{-4}{-3} = \frac{4}{3}$$
2. For points (2, 3) and (2, 7):
In this case, you would notice that both points have the same x-value. Therefore, the slope is undefined, which means the line is vertical.

### Conclusion
The slope of a line gives you a clear idea of its steepness and direction. Mastering this concept enables you to tackle more complex problems in algebra and beyond. If you have any more questions about slope or related topics, don't hesitate to ask!