The equation of the line passing through (1,-2) and parallel to the line 8x-4y+7=0 is

Options

A. 2x+y-4=0
B. 2x-y+4=0
C. 2x-y-4=0
D. 2x-y+6=0

Answer

To find the equation of the line passing through the point (1, -2) and parallel to the line given by the equation \(8x - 4y + 7 = 0\), we can follow these steps:

### Step 1: Identify the slope of the given line
The equation of the line is given in the standard form \(Ax + By + C = 0\). We can rewrite the given equation \(8x - 4y + 7 = 0\) in slope-intercept form \(y = mx + b\) to find the slope \(m\).

Starting with:
\[ 8x - 4y + 7 = 0 \]

Rearranging gives:
\[ -4y = -8x - 7 \]
\[ y = 2x + \frac{7}{4} \]

From this, we see that the slope \(m\) of the given line is \(2\).

### Step 2: Use the slope to write the equation of the parallel line
Since parallel lines have the same slope, the slope of the line we want to find is also \(2\). We can use the point-slope form of the line equation, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is the point through which the line passes, and \(m\) is the slope.

Substituting \(m = 2\) and the point \((1, -2)\):
\[ y - (-2) = 2(x - 1) \]
\[ y + 2 = 2(x - 1) \]

### Step 3: Simplify the equation
Now, we simplify the equation:
\[ y + 2 = 2x - 2 \]
\[ y = 2x - 4 \]

### Step 4: Convert to standard form
To convert this equation into standard form \(Ax + By + C = 0\), we rearrange it:
\[ 2x - y - 4 = 0 \]

### Step 5: Finalize the equation
We can multiply through by 2 to eliminate fractions if needed, but in this case, we can leave it as:
\[ 2x - y - 4 = 0 \]

Thus, the equation of the line passing through the point (1, -2) and parallel to the line \(8x - 4y + 7 = 0\) is:
\[ 2x - y - 4 = 0 \]