`2x+3y-5=0` is the regression equation of x on y. Find its slope

Answer

To find the slope of the regression equation \(2x + 3y - 5 = 0\) of \(x\) on \(y\), we can follow these steps:

### Step 1: Write the regression equation
The given regression equation is:
\[ 2x + 3y - 5 = 0 \]

### Step 2: Rearrange the equation to isolate \(x\)
We want to express \(x\) in terms of \(y\). To do this, we can rearrange the equation:
\[ 2x = -3y + 5 \]
Now, divide both sides by 2:
\[ x = \frac{5}{2} - \frac{3}{2}y \]

### Step 3: Identify the slope
In the equation \(x = \frac{5}{2} - \frac{3}{2}y\), we can see that it is in the form:
\[ x = A + By \]
where \(A = \frac{5}{2}\) (the constant term) and \(B = -\frac{3}{2}\) (the coefficient of \(y\)).

Here, the slope of the regression line of \(x\) on \(y\) is given by the coefficient of \(y\), which is:
\[ \text{slope} = -\frac{3}{2} \]

### Final Answer
Thus, the slope of the regression equation \(2x + 3y - 5 = 0\) of \(x\) on \(y\) is:
\[ -\frac{3}{2} \]

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