Using a Point and Slope, use the point on the line and the...

Using a Point and Slope, use the point on the line and the slope $m$ of the line to find three additional points through which the line passes. (There are many correct answers.)
$$(-1,-6), \quad m=-\frac{1}{2}$$

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Key Concepts

Slope

The slope of a line, represented by 'm', is a measure of how steep the line is; it is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Understanding the slope allows you to determine how much the y-coordinate changes for a given change in the x-coordinate.

Point-Slope Form

The point-slope form of a line's equation is a way to express the line's equation using its slope and a known point on the line. The formula y - y? = m(x - x?) directly links the coordinates of any point on the line with the slope, making it easy to calculate additional points on the line.

Using the Slope to Find Additional Points

Once you have a point and the slope, you can find other points on the line by applying the slope's rise over run. By adding or subtracting the run (x-increment) and the corresponding rise (y-increment) from the given point, you can generate new points that lie on the line. This method is a fundamental technique in graphing and understanding linear relationships.

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