Final answer:
The question is about identifying the type of function and the slope for an absolute value function. The function under discussion is piecewise-linear with a slope of +/-1/2, reflecting different behaviors on either side of the vertex.
Step-by-step explanation:
The question pertains to determining the type of function and slope given an equation involving absolute values. The provided equation is y = -1/2 | x-3 | + 7. This is an equation of an absolute value function, which is a piecewise-linear function that appears as a 'V' shape on a graph.
The slope of the lines will be -1/2 and 1/2 due to the nature of the absolute value, which reflects the graph across the y-axis for negative inputs while maintaining a positive slope for positive inputs. In algebra, slopes are central to the behavior of linear functions, as illustrated by Figure A1, which mentions a slope of 3 indicating a rise of 3 units on the y-axis for every 1 unit increase on the x-axis.
This concept is essential in understanding how to graph linear functions using slope and y-intercept. However, for absolute value functions like the one given, the slope describes the steepness of the 'V' shape rather than just a single line.