Find the `Y-` intercept of the line `2y=4x-3`.

Answer

To find the Y-intercept of the line given by the equation \(2y = 4x - 3\), we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
We start with the equation:
\[ 2y = 4x - 3 \]
To convert this into slope-intercept form, we need to isolate \(y\).

### Step 2: Divide both sides by 2
To isolate \(y\), we divide the entire equation by 2:
\[ y = \frac{4x - 3}{2} \]
This simplifies to:
\[ y = \frac{4}{2}x - \frac{3}{2} \]
Which further simplifies to:
\[ y = 2x - \frac{3}{2} \]

### Step 3: Identify the Y-intercept
In the slope-intercept form \(y = mx + c\), \(m\) is the slope and \(c\) is the Y-intercept. From our equation:
\[ y = 2x - \frac{3}{2} \]
We can see that the Y-intercept \(c\) is \(-\frac{3}{2}\).

### Conclusion
Thus, the Y-intercept of the line \(2y = 4x - 3\) is:
\[ \boxed{-\frac{3}{2}} \]

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