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The slope of a line is a measure of how steep the line is. It represents the change in the y-coordinate for every unit of change in the x-coordinate. To find the slope between two points, we use the slope formula. This formula is:

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

In this formula, \( x_1 \) and \( y_1 \) are the coordinates of the first point, while \( x_2 \) and \( y_2 \) are the coordinates of the second point. When you subtract the y-coordinates and divide by the difference of the x-coordinates, you get the slope.

This formula works whether you have whole numbers or fractions. By following the steps correctly, you can always find the slope between any two given points.

Coordinate geometry is a branch of geometry where points are defined and their relationships explored using the Cartesian coordinate system. This system uses two numerical coordinates to define a point's position on a plane.

The Cartesian coordinate system comprises two perpendicular axes:

• The x-axis (horizontal)
• The y-axis (vertical)

Each point on the plane is representable as (x, y), where x is the horizontal distance from the origin, and y is the vertical distance.

When finding the slope between two points, plotting these points on the coordinate plane can be helpful. It allows you to see the visual rise over run, aiding you in understanding the physical meaning of the slope. Also, coordinate geometry is crucial for graphing lines, curves, and figuring out various geometric properties directly from coordinates.

When dealing with fractions, it's essential to simplify them to make calculations easier. In the slope formula, you often subtract fractions, which necessitates a clear understanding of fractions simplification.

• First, find the least common denominator (LCD) for the fractions involved.
• Convert the fractions to have this common denominator.
• Perform the required arithmetic operations.

In the given exercise, we simplified \(\frac{11}{20} - \frac{9}{10}\) by converting \(\frac{9}{10}\) to an equivalent fraction with a common denominator of 20. Similar steps were taken for the denominator.

Finally, when dividing fractions, remember to multiply by the reciprocal of the divisor. This simplifies our result into an easy-to-understand slope value. Practice regularly with fractions, and soon you'll find these steps intuitive!