If x and y are related by 2x+3y+4 = 0 and SD of x is 9, then SD of y is

Given information:
- The equation relating x and y is 2x + 3y + 4 = 0.
- The standard deviation (SD) of x is 9.

Calculating the SD of y:
To calculate the SD of y, we need to find the relationship between x and y in the given equation. Let's rearrange the equation to solve for y:

2x + 3y + 4 = 0
3y = -2x - 4
y = (-2/3)x - 4/3

This equation shows that y is a linear function of x with a slope of -2/3 and a y-intercept of -4/3.

Understanding the relationship between SD and linear functions:
In a linear function, the SD of the dependent variable (y) is related to the SD of the independent variable (x) by the slope of the function. The SD of y is equal to the SD of x multiplied by the absolute value of the slope of the function.

Calculating the SD of y:
In this case, the slope of the function is -2/3. Therefore, the SD of y is:

SD of y = Absolute value of slope × SD of x

SD of y = |(-2/3)| × 9

SD of y = (2/3) × 9

SD of y = 6

Conclusion:
The SD of y is 6. The SD of y is determined by the absolute value of the slope of the linear function and the SD of x. In this case, since the slope is -2/3 and the SD of x is 9, the SD of y is calculated to be 6.