The equation of a line AB is `2x - 2y + 3 = 0.`
Calculate the angle that the line AB makes with the positive direction of the x-axis. 

Answer

To calculate the angle that the line AB makes with the positive direction of the x-axis from the given equation \(2x - 2y + 3 = 0\), we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The given equation is:
\[ 2x - 2y + 3 = 0 \]
We need to rearrange this into the form \(y = mx + c\), where \(m\) is the slope of the line.

### Step 2: Isolate \(y\)
To isolate \(y\), we can rearrange the equation:
\[ -2y = -2x - 3 \]
Now, divide everything by -2:
\[ y = x + \frac{3}{2} \]

### Step 3: Identify the slope
From the equation \(y = x + \frac{3}{2}\), we can see that the slope \(m\) is equal to 1.

### Step 4: Relate the slope to the angle
The slope \(m\) is related to the angle \(\theta\) that the line makes with the positive x-axis by the formula:
\[ m = \tan(\theta) \]
Since we found that \(m = 1\), we have:
\[ \tan(\theta) = 1 \]

### Step 5: Calculate the angle
To find \(\theta\), we take the arctangent:
\[ \theta = \tan^{-1}(1) \]
The angle whose tangent is 1 is:
\[ \theta = 45^\circ \]

### Final Answer
Thus, the angle that the line AB makes with the positive direction of the x-axis is:
\[ \theta = 45^\circ \]

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