The graph of the linear equation `2y = 4x – 5` passes through the point

Options

A. `(3,7/2)`
B. `(0,2)`
C. `(2,1)`
D. `(-3/2,7/2)`

Answer

To determine which point the graph of the linear equation \(2y = 4x - 5\) passes through, we will check each of the given coordinates by substituting the values of \(x\) and \(y\) into the equation.

### Step-by-Step Solution:

1. **Rewrite the Equation**:
The given equation is \(2y = 4x - 5\). We can rewrite it in the slope-intercept form \(y = mx + b\) for easier interpretation, but for this problem, we will directly substitute the values.

2. **Check Each Option**:
We will substitute the coordinates from each option into the equation to see if the left-hand side equals the right-hand side.

**Option 1**: (3, 1)
- Substitute \(x = 3\) and \(y = 1\):
\[ 2(1) = 4(3) - 5 \]
\[ 2 = 12 - 5 \]
\[ 2 = 7 \quad \text{(False)} \]

**Option 2**: (0, 2)
- Substitute \(x = 0\) and \(y = 2\):
\[ 2(2) = 4(0) - 5 \]
\[ 4 = 0 - 5 \]
\[ 4 = -5 \quad \text{(False)} \]

**Option 3**: (2, 1)
- Substitute \(x = 2\) and \(y = 1\):
\[ 2(1) = 4(2) - 5 \]
\[ 2 = 8 - 5 \]
\[ 2 = 3 \quad \text{(False)} \]

**Option 4**: (-3/2, 7/2)
- Substitute \(x = -\frac{3}{2}\) and \(y = \frac{7}{2}\):
\[ 2\left(\frac{7}{2}\right) = 4\left(-\frac{3}{2}\right) - 5 \]
\[ 7 = -6 - 5 \]
\[ 7 = -11 \quad \text{(False)} \]

3. **Conclusion**:
After checking all options, we find that none of the provided coordinates satisfy the equation \(2y = 4x - 5\). Therefore, the graph of the linear equation does not pass through any of the given points.