Find the parallel line of x - 2y = 4 that passes through the point (0, -4).

Steps to Solve

1. Convert the given line to slope-intercept form

We start with the given equation of the line:

$$ x - 2y = 4 $$

We will rearrange it to find the slope (m).

Subtract $x$ from both sides:

$$ -2y = -x + 4 $$

Now, divide by -2:

$$ y = \frac{1}{2}x - 2 $$

From this, we can see that the slope $m$ of the given line is $\frac{1}{2}$.

2. Use the point-slope form to find the new line's equation

Since the parallel line has the same slope, we will use the point-slope form of a line, which is given by:

$$ y - y_1 = m(x - x_1) $$

Here, we have the slope $m = \frac{1}{2}$ and the point $(0, -4)$, which gives us $x_1 = 0$ and $y_1 = -4$. Substitute these values into the equation:

$$ y - (-4) = \frac{1}{2}(x - 0) $$

Simplifying this, we get:

$$ y + 4 = \frac{1}{2}x $$

3. Rearranging to slope-intercept form

Now we will isolate $y$ to write the equation in slope-intercept form:

$$ y = \frac{1}{2}x - 4 $$

This is the equation of the line that is parallel to the given line and passes through the point (0, -4).