Question

The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.

Answer 1

Answer is y = -2x + 45
Assuming this is what you were looking for.

We know points (6,33) (15,15) are on the line, we can use them to find slope using slope formula y2 - y1 over x2 - x1

15 - 33 over 15 - 6 = -18/9 or -2 slope

Using slope and the y intercept of 45 (where the line crosses the y axis) we can find the equation.
y = mx + b

y = -2x + 45

If we take one set of points and substitute them into our equation we can prove our equation.

15 = -2(15) + 45

15 = -30 + 45

15 = 15 they agree so problem solved!