Final answer:
The slope of a line indicates its direction and steepness. A slope of 0 is a horizontal line, an undefined slope corresponds to a vertical line, and slopes of 1 or -1 indicate lines at 45 or -45 degrees to the x-axis, respectively.
Step-by-step explanation:
The slope of a line can tells us much about its orientation and direction on a coordinate plane. A slope = 0 signifies a horizontal line, which has no rise over its run, meaning it does not go up or down as it moves along the x-axis. When the slope is described as undefined, it means we are dealing with a vertical line where the rise over the run is not computable since the run is zero.
A slope = 1 signifies that the line rises one unit vertically for every one unit it moves horizontally to the right, indicating a positive slope and a 45-degree angle with respect to the x-axis. Conversely, a slope = -1 shows a line that falls one unit vertically for every one unit it moves horizontally to the right, therefore, indicating a negative slope and a -45-degree angle with respect to the x-axis.
According to Figure A1 Slope and the Algebra of Straight Lines, we understand that a line's slope is consistent along its entire length. The figure illustrates a line with a positive slope where the y-intercept is 9, meaning the line crosses the y-axis at the point (0, 9), and the slope is 3, indicating a rise of 3 units for every 1 unit of run along the horizontal axis.