Final answer:
To find the value of k when y varies directly with x, we can use the formula y = kx and solve for k using the given values. The value of k is 3/8 or 0.375.
Step-by-step explanation:
To find the value of k when y varies directly with x, we can use the formula y = kx. In this case, we know that y = 5 1/4 when x = 14. We can plug these values into the formula and solve for k:
5 1/4 = k * 14
To simplify the equation, let's convert 5 1/4 to an improper fraction: 5 1/4 = 21/4.
Now we have: 21/4 = 14k
To solve for k, we can multiply both sides of the equation by 4/14:
k = (21/4) / (14/1)
Simplifying the expression on the right side, we get: k = 3/8 or k = 0.375.