In order to find the equation, you need to find two things. The y intercept, and the slope. Let's start with slope.
Slope is y/x, so 1-(-5)/8-(-3) = 6/11
This means -A/B = 6/11 (I think some part of the copy and paste didn't show up for the "is positive" part)
This means A and B equal -6,11 or 6,-11
Now for C, We can use one of the coordinates given. Let's use (8,1). -48 + 11 = C, C = -37. Note that if we used the other A and B, C would be 37.
Hope that helped :)
Let A be the number of adult tickets and C be the amount of children tickets. We can form the equation 105A + 60C = 7155, as we converted it from dollars to regular integers. We can simplify the equation by dividing by 5, giving 21A + 12C = 1431. Dividing by 3 gives 7A + 4C = 477. 477 divided by 7 gives 68 remainders 1, and if we remove one more seven and add it to one, we will have a multiple of 4. This means 67 adult tickets and 2 children tickets.