Use the point on the line and the slope of the line to find...

Use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.)
$$
\begin{array}{ll}{\text { Point }} & {\text { Slope }} \\ {\text { (-1,-6) }} & {m=-\frac{1}{2}}\end{array}
$$

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Key Concepts

Slope

Slope is a measure of how steep a line is, defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points. It indicates the direction of the line: a positive slope means the line rises as it moves right, whereas a negative slope means it falls, and a zero slope indicates a horizontal line.

Point-Slope Form

The point-slope form of a linear equation is a formula used to write the equation of a line when given a point on the line and the slope. It is expressed as y - y? = m(x - x?), where (x?, y?) is a known point and m is the slope. This form is particularly useful for easily finding the line’s equation or generating additional points on the line.

Calculating Additional Points

To calculate additional points on a line given a point and the slope, one can use the concept of rise and run. Starting from the known point, adjust the x-coordinate by adding (or subtracting) a chosen value and then adjust the y-coordinate based on the slope (multiplying the change in x by the slope). Repeating this process with different increments allows you to identify multiple points that lie on the line.

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