Answer
The decreasing order of the slope is ${{m}_{1}}>{{m}_{3}}>{{m}_{2}}>{{m}_{4}}$.
Work Step by Step
The slope of a line can be defined as the rate of change of y with respect to x. A line is said to have a positive slope when the value of y increases with an increase in x and decreases with a decrease in x. In this case, the line will rise from left to right. Also, the steepest line has the highest slope.
From the given figure, it can be seen that the line $y={{m}_{1}}x+{{b}_{1}}$ is the steepest and rising from left to right. That means that its y coordinate increases at the fastest rate. Therefore, the line $y={{m}_{1}}x+{{b}_{1}}$ has the highest slope.
Also, the line $y={{m}_{3}}x+{{b}_{3}}$ is steep and rising from left to right. But its steepness is less than $y={{m}_{1}}x+{{b}_{1}}$. Therefore, $y={{m}_{3}}x+{{b}_{3}}$ has a slope less than that of $y={{m}_{1}}x+{{b}_{1}}$.
The slope of a line is the rate of change of y with respect to x.
A line has a negative slope when the value of y decreases with an increase in x and increases with a decrease in x. In this case, the line falls from left to right. Also, the least steepest line has the highest slope.
From the given figure, it can be seen that the line $y={{m}_{2}}x+{{b}_{2}}$ falls from left to right and its steepness is less than that of $y={{m}_{4}}x+{{b}_{4}}$. Therefore, line $y={{m}_{2}}x+{{b}_{2}}$ has a slope less than that of $y={{m}_{3}}x+{{b}_{3}}$.
Also, the line $y={{m}_{4}}x+{{b}_{4}}$ is steeper and falls from left to right. Therefore, $y={{m}_{4}}x+{{b}_{4}}$ has a slope less than that of $y={{m}_{2}}x+{{b}_{2}}$.
Hence, the slopes in decreasing order are ${{m}_{1}},\ {{m}_{3}},\ {{m}_{2}},\ {{m}_{4}}$.
