### Instruction: The line $ax+(a+1)y=a+2$ passes through the point $(4,-8)$. Find $a$.### Response: I see that this is a problem involving a linear equation and a given point on the line.
I want to find the value of $a$ that makes the equation true for the coordinates of the point.
To do this, I can substitute the $x$ and $y$ values of the point into the equation and solve for $a$.
So, plugging in $x=4$ and $y=-8$, I get $a(4)+(a+1)(-8)=a+2$.
I need to simplify and solve for $a$.
Expanding the brackets, I get $4a-8a-8=a+2$.
Combining like terms, I get $-4a-8=a+2$.
Subtracting $a$ from both sides, I get $-5a-8=2$.
Adding $8$ to both sides, I get $-5a=10$.