Find the equation of a line passing through (-4, 1)and making equal intercepts on the coordinates axis

Options

A. ` x + 2 y + 3 = 0`
B. ` x + y - 7 = 0 `
C. ` 2 x - y + 8 = 0 `
D. ` x + y + 3 = 0`

Answer

To find the equation of a line passing through the point (-4, 1) and making equal intercepts on the coordinate axes, we can follow these steps:

### Step 1: Understand the concept of equal intercepts
A line that makes equal intercepts on the coordinate axes has the form \( x + y = c \), where \( c \) is a constant. This means that the x-intercept and y-intercept are equal.

### Step 2: Write the general equation
The general equation of a line with equal intercepts can be expressed as:
\[ y + x = c \]

### Step 3: Substitute the point into the equation
Since the line passes through the point (-4, 1), we can substitute \( x = -4 \) and \( y = 1 \) into the equation:
\[ 1 + (-4) = c \]

### Step 4: Solve for \( c \)
Now, calculate the value of \( c \):
\[ 1 - 4 = c \]
\[ c = -3 \]

### Step 5: Write the specific equation of the line
Now that we have the value of \( c \), we can write the specific equation of the line:
\[ y + x = -3 \]

### Step 6: Rearrange the equation
To express the equation in a standard form, we can rearrange it:
\[ y + x + 3 = 0 \]

Thus, the final equation of the line is:
\[ x + y + 3 = 0 \]