**Introduction:**

To find the equation of a straight line, we need information about the intercepts it makes with the axes of coordinates. In this case, we are given that the portion of the straight line intercepted between the axes is bisected at the point (2p, 2q). Let's proceed step by step to find the equation of the straight line.

**Step 1: Find the coordinates of the mid-point:**

We are given that the portion of the straight line intercepted between the axes is bisected at the point (2p, 2q). This means that the mid-point of the line segment is (2p, 2q).

**Step 2: Find the coordinates of the intercepts:**

Since the line is intercepted by both the x-axis and y-axis, we need to find the coordinates of these intercepts.

- X-intercept: The x-intercept is the point where the line intersects the x-axis. Since the y-coordinate of this point is 0, the x-intercept can be represented as (x, 0).
- Y-intercept: The y-intercept is the point where the line intersects the y-axis. Similarly, the y-intercept can be represented as (0, y).

**Step 3: Use the midpoint formula:**

According to the midpoint formula, the coordinates of the mid-point can be found using the following equation:

Mid-point = ((x1 + x2)/2, (y1 + y2)/2)

In this case, we know the mid-point is (2p, 2q). We can equate the coordinates and solve for x and y:

(2p, 2q) = ((x + 0)/2, (y + 0)/2)

Simplifying the equation, we get:

2p = x/2
2q = y/2

Multiplying both sides by 2, we obtain:

4p = x
4q = y

**Step 4: Write the equation of the straight line:**

Now that we have the coordinates of the intercepts, we can write the equation of the straight line using the slope-intercept form, which is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

In this case, the slope (m) can be determined using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the intercepts, we get:

m = (4q - 0) / (4p - 0)
m = q/p

Finally, substituting the slope and the y-intercept (0, y), we can write the equation of the straight line as:

y = (q/p)x + y

Therefore, the equation of the straight line intercepted between the axes of coordinates and bisected at (2p, 2q) is:

y = (q/p)x + y