Final answer:
The slope of a line on the coordinate plane indicates its direction; positive slopes tilt upwards, negative slopes downwards, zero slopes are flat and horizontal, and undefined slopes represent vertical lines.
Step-by-step explanation:
The slope of a line on the coordinate plane can indicate whether a line is increasing or decreasing as it moves from left to right. A positive slope implies that the line moves upward on the y-axis as the x-value increases, indicating a rise over run. For example, in Figure A1, the line graph has a slope of 3, meaning for every increase of 1 on the x-axis (horizontal), there is a rise of 3 on the y-axis (vertical), making it a straight line with positive slope.
A negative slope, in contrast, means the line moves downward as one moves to the right along the x-axis. A slope of zero indicates a horizontal line, which is perfectly flat and neither rises nor falls as it moves to the right. An undefined slope is characteristic of a vertical line, where dividing the change in y by the change in x (rise over run) is not possible because the change in x is zero and division by zero is undefined.
The appearance of these slopes on a graph can be summarized as follows: Lines with positive slopes tilt upwards, lines with negative slopes tilt downwards, a line with a zero slope is flat and horizontal, and a line with an undefined slope is perfectly vertical.