The intercept cut off from Y-axis is twice that from X-axis by the line and line passes through `(1,2),` then its equation is

Options

A. `2x +y=4`
B. `2x+y+4=0`
C. `2x-y=4`
D. `2x-y+4 =0`

Answer

To find the equation of the line that has a y-intercept which is twice that of the x-intercept and passes through the point (1, 2), we can follow these steps:

### Step 1: Define the intercepts
Let the x-intercept be \( a \) and the y-intercept be \( b \). According to the problem, we have:
\[ b = 2a \]

### Step 2: Write the equation of the line in intercept form
The equation of a line in intercept form is given by:
\[ \frac{x}{a} + \frac{y}{b} = 1 \]

### Step 3: Substitute \( b \) in the equation
Substituting \( b = 2a \) into the intercept form equation, we get:
\[ \frac{x}{a} + \frac{y}{2a} = 1 \]

### Step 4: Clear the denominators
To eliminate the denominators, multiply the entire equation by \( 2a \):
\[ 2x + y = 2a \]

### Step 5: Use the point (1, 2) to find \( a \)
Since the line passes through the point (1, 2), we substitute \( x = 1 \) and \( y = 2 \) into the equation:
\[ 2(1) + 2 = 2a \]
This simplifies to:
\[ 2 + 2 = 2a \]
\[ 4 = 2a \]
Dividing both sides by 2 gives:
\[ a = 2 \]

### Step 6: Find \( b \)
Now that we have \( a \), we can find \( b \):
\[ b = 2a = 2(2) = 4 \]

### Step 7: Write the final equation
Substituting \( a \) and \( b \) back into the equation \( 2x + y = 2a \):
\[ 2x + y = 4 \]

Thus, the equation of the line is:
\[ 2x + y = 4 \]

### Final Answer
The equation of the line is:
\[ 2x + y = 4 \]

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