If `2x+3y-1=0` is the regression line of y on x, then `b_(yx)` is ……………..

Answer

To find the regression coefficient \( b_{yx} \) from the given regression line equation \( 2x + 3y - 1 = 0 \), we can follow these steps:

### Step 1: Rearrange the equation to express \( y \) in terms of \( x \).
Starting with the equation:
\[ 2x + 3y - 1 = 0 \]

We can rearrange it to isolate \( y \):
\[ 3y = -2x + 1 \]

### Step 2: Solve for \( y \).
Now, divide each term by 3 to solve for \( y \):
\[ y = -\frac{2}{3}x + \frac{1}{3} \]

### Step 3: Identify the slope of the regression line.
In the equation \( y = mx + c \), \( m \) represents the slope. From our equation:
\[ y = -\frac{2}{3}x + \frac{1}{3} \]
we can see that the slope \( m \) is:
\[ m = -\frac{2}{3} \]

### Step 4: Conclude the value of \( b_{yx} \).
The slope of the regression line \( b_{yx} \) is equal to the slope we found:
\[ b_{yx} = -\frac{2}{3} \]

Thus, the value of \( b_{yx} \) is:
\[ \boxed{-\frac{2}{3}} \]

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