Final answer:
To find the k value and write the equation for a direct variation problem, we substitute the given values into the equation and solve for k. The k value is found to be 2, and the equation becomes y = 2x.
Step-by-step explanation:
To find the k value and write the equation, we need to use the given information. We know that x and y vary directly, and when x = 5, y = 10. In a direct variation equation, we have the form y = kx, where k is the constant of variation. To find the k value, we can substitute the given values into the equation and solve for k.
So, substituting y = 10 and x = 5 into y = kx gives us 10 = 5k. Solving for k, we divide both sides by 5 to get k = 2. Therefore, the k value is 2.
The equation for the direct variation is then y = 2x. This means that as x increases, y will increase by twice as much, and as x decreases, y will decrease by half as much.