Let variable x represents time and variable y represents distance on the coordinate plane.
The initial position is at x=0 hours and y=0 miles. The end position is at x=6 hours and y=5 miles. Then you get two points on the line with coordinates (0,0) and (6,5).
The slope can be calculated using formula
[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]
Thus, in your case
[tex]\dfrac{5-0}{6-0}=\dfrac{5}{6}.[/tex]
Answer: the slope is [tex]\dfrac{5}{6}.[/tex]
