Answer
The order of decreasing is \[{{b}_{2}}>{{b}_{1}}>{{b}_{4}}>{{b}_{3}}\].
Work Step by Step
The y-coordinate of the point, where the line intersects the y-axis is called the y-intercept.
The lines \[y={{m}_{1}}x+{{b}_{1}}\] and \[y={{m}_{2}}x+{{b}_{2}}\] cuts the y-axis at the positive side of the y-axis. Thus, \[{{b}_{1}}>0,\text{ and }{{b}_{2}}>0\]. It can be seen from the graph that \[{{b}_{2}}>{{b}_{1}}\].
The lines \[y={{m}_{3}}x+{{b}_{3}}\] and \[y={{m}_{4}}x+{{b}_{4}}\] cuts the y-axis at the negative side of the y-axis. Thus, \[{{b}_{3}}<0,\text{ and }{{b}_{4}}<0\]. It can be seen from the graph that \[{{b}_{4}}>{{b}_{3}}\].
Also, \[{{b}_{1}}>{{b}_{4}}\]
Therefore, the order of decreasing size of the y-intercepts is \[{{b}_{2}}>{{b}_{1}}>{{b}_{4}}>{{b}_{3}}\].
