The line `y = 2x +4` is shifted 2 units along `+y` axis, keeping parallel to itself and then 1 unit along `+x` axis direction in the same manner, then equation of the line in its new position is,

Options

A. `y = 2x +6`
B. `y = 2x +5`
C. `y = 2x +4`
D. none of these

Explanation

To solve the problem step by step, we will follow the transformations of the line given by the equation \( y = 2x + 4 \).

### Step 1: Identify the original line equation
The original line is given by:
\[ y = 2x + 4 \]

### Step 2: Shift the line 2 units along the +y axis
When we shift a line parallel to itself along the y-axis, we add the shift value to the y-coordinate. Therefore, shifting the line 2 units up means we replace \( y \) with \( y - 2 \) in the equation:
\[ y + 2 = 2x + 4 \]

### Step 3: Rearranging the equation after the first shift
Now, we can rearrange the equation:
\[ y = 2x + 4 - 2 \]
\[ y = 2x + 2 \]

### Step 4: Shift the line 1 unit along the +x axis
Next, we shift the line 1 unit to the right along the x-axis. This means we replace \( x \) with \( x - 1 \):
\[ y = 2(x - 1) + 2 \]

### Step 5: Simplify the equation after the second shift
Now, we simplify the equation:
\[ y = 2x - 2 + 2 \]
\[ y = 2x \]

### Final Result
Thus, the equation of the line in its new position after both shifts is:
\[ y = 2x \]