In the following exercises, (a) find the slope of the line...

In the following exercises,
(a) find the slope of the line passing through each pair of points, if possible, and
(b) based on the slope, indicate whether the line rises from left to right, falls from left to right, is horizontal, or is vertical.
$$
(-4,1) \text { and }(-3,4)
$$

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Key Concepts

Slope

Slope is a measure of the steepness and direction of a line in the coordinate plane. It is calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). The slope tells you how much the y-coordinate of a point on the line increases (or decreases) as the x-coordinate increases.

Calculation from Two Points

When given two points, the slope is computed by subtracting the y-coordinate of the first point from the y-coordinate of the second point, and similarly subtracting the x-coordinate of the first point from the x-coordinate of the second point, then taking the ratio of these differences. This calculation is fundamental in coordinate geometry for describing the linear relationship between points.

Line Orientation

The orientation of a line refers to how the line is positioned in the plane based on its slope. If the slope is positive, the line rises from left to right; if it is negative, the line falls from left to right. A zero slope indicates a horizontal line, while an undefined slope (due to division by zero) indicates a vertical line.

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