Final answer:
The main characteristics of linear function graphs are the slope, representing the line's steepness, and the y-intercept, where the line crosses the y-axis.
Step-by-step explanation:
The main characteristics used when describing graphs of linear functions are slope and y-intercept. The slope indicates the steepness of a line and is represented by the coefficient of x (m or b) in the linear equation of the form y = mx + b or y = a + bx, with m or b being the slope. The y-intercept is the point where the line crosses the y-axis, corresponding to the constant term in the equation. To visualize this, consider a straight line on a graph with perpendicular axes: if the slope is 3, there is a rise of 3 units on the y-axis for each increase of 1 unit along the x-axis, and the y-intercept would be the y-coordinate where the line meets the y-axis.