10. A line intersects the $y$-axis, the line $y=2 x+2$, and the $x$-axis at the points $A, B$, and $C$, respectively. If segment $A C$ has a length of $4 \sqrt{2}$ units and $B$ lies in the first quadrant and is the midpoint of segment $A C$, find the equation of the line in slope-intercept form.
10. $y=-7 x+\frac{28}{5}$