Final answer:
d is the correct option. The question appears to have a typo, as slope is determined between two points, not three. To find the slope, one would use the change in y divided by the change in x. Based on Figure A1, the slope of the line is 3, which represents a consistent positive slope.
Step-by-step explanation:
To find the slope of a line segment given two points, use the formula:
slope (m) = (change in y) / (change in x)
However, the question asks for the slope of the line segment of the points x, y, z, which appears to be a typo since a line segment's slope is defined only between two points in a two-dimensional space, typically written as (x1, y1) and (x2, y2).
Based on the formula and the information provided in the Figure A1 excerpt, the slope of a straight line can be calculated using:
m = rise / run
With the given information that a line has a y-intercept of 9 and a slope of 3, this means for every increase in x by 1, y increases by 3. Hence, the slope is constant at 3, which is option "b" in an illustrative example provided, indicating a straight line with a positive slope.
If we ignore the typo in the original question, the correct answer from the provided options would be:
d) z−y/x−z
But this assumes that x, y, and z represent points on a coordinate plane in a specific manner, which is not clarified in the question. Therefore, in context of the information given, the correct option for the slope of a line segment between two points is not listed in the choices provided, assuming a traditional interpretation of x and y as coordinate points.