If the x-intercept of some line L is double as that of the line, 3x+4y=24 and the y-intercept of L is half as that of the same line, then the slope of L is

We are given that the x-intercept of line L is twice that of the line 3x + 4y = 24, and the y-intercept of line L is half of that of the same line. We need to find the slope of line L.

Step 1: Find the intercepts of the given line (3x + 4y = 24)
To find the x-intercept, set y = 0 in the equation 3x + 4y = 24:

3x + 4(0) = 24
3x = 24
x = 8

So, the x-intercept of the given line is 8.

To find the y-intercept, set x = 0 in the equation 3x + 4y = 24:

3(0) + 4y = 24
4y = 24
y = 6

So, the y-intercept of the given line is 6.

Step 2: Use the conditions for line L
The x-intercept of line L is double that of the given line, so the x-intercept of line L is 2 * 8 = 16.
The y-intercept of line L is half that of the given line, so the y-intercept of line L is (1/2) * 6 = 3.
Step 3: Write the equation of line L
The equation of a line in intercept form is:

x/x-intercept + y/y-intercept = 1

For line L, the intercepts are 16 and 3. So, the equation of line L is:

x/16 + y/3 = 1

Step 4: Rearrange to find the slope
Rearranging the equation of line L to the slope-intercept form (y = mx + c):

y/3 = 1 - x/16
y = 3(1 - x/16)
y = 3 - 3x/16

So, the slope of the line is the coefficient of x, which is -3/16.

Final Answer:
The slope of line L is -3/16.