Question 1195435
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rise = change in height
run = change in horizontal direction


{{{slope = rise/run}}}


{{{9 <= rise <= 10}}}


{{{18 <= run <= 24}}}


To get the smallest slope possible, we divide the smallest rise over the largest run.
We divide rise = 9 over run = 24 to get the smallest slope.
Recall that A/B is smallest when we minimize A and maximize B. Both are positive values. 


P = smallest slope
{{{P = 9/24}}}
{{{P = (3*3)/(3*8)}}}
{{{P = 3/8}}}


In contrast, the largest slope occurs when we go for the largest rise and smallest run
Q = largest slope
{{{Q = 10/18}}}
{{{Q = (2*5)/(2*9)}}}
{{{Q = 5/9}}}


Therefore we can say
{{{P <= slope <= Q}}}


{{{3/8 <= slope <= 5/9}}}


Convert each slope to decimal form
3/8 = 0.375
5/9 = 0.556 approximately


So,
{{{3/8 <= slope <= 5/9}}}
{{{0.375 <= slope <= 0.556}}}


We can see that choices C and D can be ruled out because they are the endpoints mentioned earlier. 


Choice B) 5/12 converts to the approximate decimal form of 0.417 and it is between those endpoints mentioned above. So we can rule out choice B


Choice A) 1/3 = 0.333 approximately is NOT between 3/8 = 0.375 and 5/9 = 0.556
The slope mentioned for choice A is too small, aka too shallow.


Answer: <font color=red>Choice A) 1/3</font>
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