Answer
The order of decreasing is \[{{m}_{1}}>{{m}_{3}}>{{m}_{2}}>{{m}_{4}}\].
Work Step by Step
In the figure, the lines \[y={{m}_{1}}x+{{b}_{1}}\] and \[y={{m}_{3}}x+{{b}_{3}}\] rises from left to right and the lines \[y={{m}_{2}}x+{{b}_{2}}\] and \[y={{m}_{4}}x+{{b}_{4}}\] falls from left to right. Thus, \[{{m}_{1}}>0,\text{ and }{{m}_{3}}>0\] and \[{{m}_{2}}<0,\text{ and }{{m}_{4}}<0\].
The line, \[y={{m}_{1}}x+{{b}_{1}}\] rises high as compared to the line, \[y={{m}_{3}}x+{{b}_{3}}\]. So, \[{{m}_{1}}>{{m}_{3}}\].
The line \[y={{m}_{4}}x+{{b}_{4}}\] falls lower as compared to the line, \[y={{m}_{2}}x+{{b}_{2}}\]. So, \[{{m}_{2}}>{{m}_{4}}\].
Also, \[{{m}_{3}}>{{m}_{2}}\]
Therefore, the order of decreasing size of slopes is \[{{m}_{1}}>{{m}_{3}}>{{m}_{2}}>{{m}_{4}}\].
