Question

A faucet is used to add water to a large bottle that already contained some water. after it has been filling for 4 ​seconds, the gauge on the bottle indicates that it contains 12 ounces of water. after it has been filling for 11 ​seconds, the gauge indicates the bottle contains 26 ounces of water. let y be the amount of water in the bottle x seconds after the faucet was turned on. write a linear equation that relates the amount of water in the​ bottle, y, to the time x.

Answer 1

The problem gives us points (4, 12) and (11,26). We first find the slope using m=(y2-y1)/(x2-x1). We substitute and get m=(26-12)/(11-4). This simplifies to m = 2. We can then use the point-slope form y-y1 = m(x-x1). We substitute and get y - 12 = 2(x - 4). We distribute: y - 12 = 2x - 8. We add 12 to both sides to get our final answer, y = 2x + 4.