Question

PLZ HELP ME QUICKLY EXPLAIN

Answer 1

This is a nice problem to test the understanding of the translation of a function.
In general, a transformation
f(x)->g(x) where g(x)=f(x-h)+k
involves a translation of h units to the right, and k unit up.

In the case of a straight line, we do not see separate effects of horizontal or vertical translations, because the image g(x) remains parallel to the original function f(x).

The translation of f(x)=-2x+7 -> g(x)=f(x-h)+k 
can be visualized as
g(x)=-2(x-h)+7+k
which by expansion
g(x)=-2x+2h+7+k
Since we have the image 9 units BELOW f(x), we equate
f(x)-9=-2x+2h+7+k=g(x)
=>
-2x+7-9=-2x+2h+7+k
on simplification =>
2h+k=-9
From the given answer options,
a. h=-5, k=1 => 2h+k=-10+1=-9  [ equals -9, so OK]
b. h=4, k=1 => 2h+k=8+1=9        [does not equal -9, so NOT THIS ONE]
c. h=-2, k=2 => 2h+k=-4+2=-2     [does not equal -9, so NOT THIS ONE]
d. h=-9, k=2 => 2h+k=-18+2=-18  [does not equal -9, so NOT THIS ONE]