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 given that the intercept cut off from the Y-axis is twice that from the X-axis and that the line passes through the point (1, 2), we can follow these steps:

### Step 1: Define the intercepts
Let the intercept on the X-axis be \( a \). According to the problem, the intercept on the Y-axis will be \( 2a \).

### Step 2: Write the equation of the line
Using the intercept form of the equation of a line, we have:
\[ \frac{x}{a} + \frac{y}{2a} = 1 \]

### Step 3: Substitute the point (1, 2) into the equation
Since the line passes through the point (1, 2), we can substitute \( x = 1 \) and \( y = 2 \) into the equation:
\[ \frac{1}{a} + \frac{2}{2a} = 1 \]

### Step 4: Simplify the equation
This simplifies to:
\[ \frac{1}{a} + \frac{1}{a} = 1 \]
\[ \frac{2}{a} = 1 \]

### Step 5: Solve for \( a \)
From the equation \( \frac{2}{a} = 1 \), we can solve for \( a \):
\[ 2 = a \implies a = 2 \]

### Step 6: Find the Y-intercept
Now, since \( b = 2a \):
\[ b = 2 \times 2 = 4 \]

### Step 7: Write the final equation
Now substituting \( a \) and \( b \) back into the intercept form:
\[ \frac{x}{2} + \frac{y}{4} = 1 \]

### Step 8: Rearranging the equation
To express it in a standard form, we can multiply through by 4:
\[ 2x + y = 4 \]

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