Introduction:
In this problem, we are required to find the equation of a straight line which passes through the point (3,-2) and cuts off positive intercept on the x-axis and y-axis which are in the ratio 4:3.

Steps:

1. Determine the intercepts
2. Calculate the ratio of intercepts
3. Write the equation of the line

Step 1: Determine the intercepts
Let the x-intercept be 4k and the y-intercept be 3k.
Using the intercept form of a line, we can write the equation as:
`(x/4k) + (y/3k) = 1`

Since the line passes through the point (3,-2), we can substitute these values to get:
`(3/4k) + (-2/3k) = 1`

Simplifying the above equation, we get:
`9 - 8k = 12k`
`20k = 9`
`k = 9/20`

Therefore, the x-intercept is `4k = (4*9)/20 = 9/5` and the y-intercept is `3k = (3*9)/20 = 27/20`.

Step 2: Calculate the ratio of intercepts
The ratio of the intercepts is given as 4:3.
Therefore, we can write:
`x-intercept/y-intercept = 4/3`

Substituting the values of the intercepts, we get:
`(9/5)/(27/20) = 4/3`

Simplifying the above equation, we get:
`x-intercept = (36/15)y-intercept`

Step 3: Write the equation of the line
We know that the equation of a line in slope-intercept form is `y = mx + c`, where m is the slope and c is the y-intercept.
We can write the equation in terms of the intercepts as:
`y = (36/15)x - (27/20)`

Simplifying the above equation, we get:
`y = (12/5)x - (27/20)`

Therefore, the equation of the line which passes through the point (3,-2) and cuts off positive intercept on the x-axis and y-axis which are in the ratio 4:3 is `y = (12/5)x - (27/20)`.

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