Final Answer:
When the line passes through the point (4, 2) with a slope of (y), the value of (a) for the point (4, a) on the line is twice the slope, as given by (a = 2y). Thus the option A) y = 2 is correct answer.
Step-by-step explanation:
To find the value of (a), we can use the point-slope form of a linear equation, which is given by (y - y_1 = m(x - x_1)), where ((x_1, y_1)) is a point on the line, and (m) is the slope. In this case, the given point is ((4, 2)), and the slope is denoted by (y).
Using the point-slope form, we have (a - 2 = y(4 - 4)). Simplifying this expression gives (a - 2 = 0), and solving for (a) yields (a = 2).
Now, comparing this result with the given options, we find that (a = 2) corresponds to option **D) a = 2y.** This means that the value of (a) is twice the slope (y).
In conclusion, the correct answer is option **D) a = 2y**, as solving the equation obtained from the point-slope form leads to (a = 2), establishing the relationship between (a) and the given slope (y).