Final answer:
The value of k varies directly with m and is calculated using the equation k = cm. Given k = 13.5 when m = 4, the constant of variation c is found to be 3.375. Therefore, when m is 28, the value of k is 94.5.
Step-by-step explanation:
The value of k varies directly with m. This means that when m increases, k also increases at the same rate. The direct variation can be written in the form of an equation: k = cm, where c is the constant of variation. To determine the constant of variation, we can use the given values when K = 13.5 and m = 4.
First, find the constant of variation by rearranging the equation: c = k / m. Plugging in the values, we get c = 13.5 / 4 = 3.375. Now that we have the constant of variation, we can use this to find the value of k when m is 28.
Using the direct variation formula and the constant of variation, the equation becomes: k = 3.375 × 28. Solve this to find that k is 94.5 when m is 28.