Question 1003286
The arrangement forms a right triangle.  The height leg is unknown.  The bottom floor leg is 9 feet.  The ladder is the hypotenuse length and is  15.  You want to find y in {{{y^2+9^2=15^2}}}.


{{{y=sqrt(15^2-9^2)=sqrt(225-81)=sqrt(144)=12}}}


Not done yet.


Slope would be {{{y/9}}}, and sign is a matter of which side you view the leaning ladder.  Slope in absolute value is {{{12/9=highlight(4/3)}}}.