Question

the graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number of days it is plugged into the wall current. which is a reasonable estimate of the constant of variation? 0.25 kwh per day 0.50 kwh per day 2.40 kwh per day 4.00 kwh per day

Explanation:

Step1: Recall the formula for direct variation

For a direct variation \(y = kx\), where \(k\) is the constant of variation. Here, \(y\) is electricity usage (in kWh) and \(x\) is the number of days. We can estimate \(k\) by finding the slope of the line.

Step2: Estimate two points on the line

Looking at the graph, assume a point \((8,2)\) (approximate values based on the grid - for example, if \(x = 8\) days and \(y=2\) kWh).

Step3: Calculate the constant of variation \(k\)

Using the formula \(k=\frac{y}{x}\), substitute \(x = 8\) and \(y = 2\). Then \(k=\frac{2}{8}=0.25\)

Answer:

0.25 kWh per day