The angle between the graph of the linear equation ` 239 x - 239 y + 5 = 0 ` and the x - axis is

Options

A. `0^(@)`
B. `60^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

To find the angle between the graph of the linear equation \( 239x - 239y + 5 = 0 \) and the x-axis, we can follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The given equation is:
\[ 239x - 239y + 5 = 0 \]

We can rearrange it to solve for \( y \):
\[ 239y = 239x + 5 \]
\[ y = x + \frac{5}{239} \]

### Step 2: Identify the slope
From the equation \( y = mx + b \), where \( m \) is the slope, we can see that:
\[ m = 1 \]

### Step 3: Relate the slope to the angle
The slope \( m \) is related to the angle \( \theta \) that the line makes with the x-axis by the formula:
\[ m = \tan(\theta) \]

Since we have \( m = 1 \):
\[ \tan(\theta) = 1 \]

### Step 4: Find the angle
To find \( \theta \), we can take the arctangent of both sides:
\[ \theta = \tan^{-1}(1) \]

The angle whose tangent is 1 is:
\[ \theta = 45^\circ \]

### Final Answer
Thus, the angle between the graph of the linear equation \( 239x - 239y + 5 = 0 \) and the x-axis is:
\[ \theta = 45^\circ \]

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