Question The number of sofas a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 455 sofas in 48 hours. What is an equation that relates the number of sofas produced, n, with the amount of time, t, in hours? What is the graph of your equation?
To find the equation that relates the number of sofas produced, n, with the amount of time, t, in hours, we can use the formula for direct variation, which is n = kt, where k is the constant of variation.
Plugging in the given data, where n = 455 and t = 48 hours, we can solve for k:
455 = k * 48
k = 455/48
k ≈ 9.479
Therefore, the equation that relates the number of sofas produced, n, with the amount of time, t, in hours is:
n = 9.479t
The graph of this equation would show a straight line passing through the origin (0,0) with a positive slope of 9.479. As the amount of time increases, the number of sofas produced will also increase in a directly proportional manner.