Final answer:
The value of n in the direct variation that includes the points (3,39) and (n,26) is found by first determining the constant of variation k from the given points and then using it to solve for n. In this case, k equals 13, and by substituting the value of y as 26 into the direct variation equation, we find that n equals 2.
Step-by-step explanation:
To find the value of n in a direct variation that includes the points (3,39) and (n,26), we first need to understand what direct variation means. A direct variation can be described by an equation of the form y = kx, where k is the constant of variation.
Since (3,39) is a point on this line, we can substitute these values into our equation to find k. Plugging in the values, we get 39 = 3k. Solving for k gives us k = 13.
Now that we have our constant of variation, we can use it to find the value of n when the y-value is 26. Substituting into the equation, we get 26 = 13n. Dividing both sides by 13, we find n equals 2. Therefore, the value of n is 2.