Final answer:
The slope of a line represents its steepness and is calculated as the ratio of rise over run. A horizontal line has a slope of 0, as illustrated by the equation y = 5, while a vertical line's slope is undefined, as shown by the equation x = 6. Figure A1 demonstrates a line with a positive slope of 3, indicating that the line rises 3 units for every unit it moves horizontally.
Step-by-step explanation:
The slope of a line in a graph is a measure of its steepness, which can be determined by the ratio of the rise (change in y-value) to the run (change in x-value) between two points on the line. For a horizontal line, all points have the same y-coordinate, which means there is no rise, considering the position of the points (1,5), (4,5), and (-2,5). Therefore, the slope is 0, and the equation is y = 5. Conversely, for a vertical line, all points have the same x-coordinate; since there is no run, the slope cannot be calculated through division by zero, and we say the slope is undefined, as in the case of points (6,-13), (6,5), and (6,22) where the equation is x = 6.
Considering Figure A1, the information provided states that the graph has an intercept on the y-axis at 9, and the slope m of the line is 3, meaning this graphical representation shows a straight line where for every increase by 1 unit on the x-axis, the line rises by 3 units on the y-axis. This consistent ratio defines the linearity of the graph.