The intercept made by a line on y-axis is double to the intercept made by it on x-axis. If it passes through (1,2) then its equation

Options

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

Answer

To find the equation of the line given that the y-intercept is double the x-intercept and that it 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 know that:
\[ b = 2a \]

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

Substituting \( b = 2a \) into the equation, we have:
\[ \frac{x}{a} + \frac{y}{2a} = 1 \]

### Step 3: Clear the denominators
To eliminate the denominators, multiply the entire equation by \( 2a \):
\[ 2a \cdot \frac{x}{a} + 2a \cdot \frac{y}{2a} = 2a \]
This simplifies to:
\[ 2x + y = 2a \]

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

### Step 5: Solve for \( a \)
Dividing both sides by 2 gives:
\[ a = 2 \]

### Step 6: Find \( b \)
Using the relationship \( b = 2a \):
\[ b = 2(2) = 4 \]

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

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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