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.)
Point$\quad$ Slope
$(-4,1) \quad m$ is undefined.

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Key Concepts

Vertical Line

A vertical line in the Cartesian plane is one where all points have the same x-coordinate. The equation of a vertical line is typically given in the form x = a, where 'a' is the constant x-value. This concept is important because it illustrates a special case in linear equations where the slope is undefined.

Finding Points on a Line

Plotting additional points on a line using a known point and the concept of slope involves using the line's defining characteristics—specifically, maintaining the same x-coordinate for vertical lines or applying the rise-over-run ratio for others. In the case of a vertical line, selecting any y-value while keeping the x-coordinate constant yields additional valid points on the line.

Undefined Slope

An undefined slope indicates that the change in x is zero while the change in y is non-zero. This situation occurs in vertical lines where the slope formula (change in y divided by change in x) results in division by zero, which is undefined. Understanding undefined slopes is crucial for recognizing vertical lines in coordinate geometry.

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