Step 1: Let $P$ divide $AB$ in the ratio $k : 1$.
Step 2: By section formula, the $y$-coordinate of $P$ is
$$y = \frac{k(9) + 1(4)}{k + 1} = \frac{9k + 4}{k + 1}$$
Step 3: Given $y = 7$ :
$$\frac{9k + 4}{k + 1} = 7$$
Step 4: Cross-multiply.
$$9k + 4 = 7k + 7 \Rightarrow 2k = 3 \Rightarrow k = \frac{3}{2}$$
Hence the required ratio is $3 : 2$.
Step 5: Now find $x$ using the section formula for the $x$-coordinate with $m : n = 3 : 2$ :
$$x = \frac{3(7) + 2(-5)}{3 + 2} = \frac{21 - 10}{5} = \frac{11}{5}$$
Hence the ratio is $3 : 2$ and $x = \dfrac{11}{5} = 2{\cdot}2$.