Question

A line passes through the point (4, 2) and has a slope of y. What is the value of a if the point (4, a) is also on the line?

A) y = 2
B) y = 4
C) a = 4
D) a = 2y

Answer 1

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).