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

Steps to Solve

1. Convert the original line equation to slope-intercept form

We start with the original line equation: $$ x + 2y = 4 $$

To convert it to slope-intercept form ($y = mx + b$), we rearrange the equation: $$ 2y = -x + 4 $$ Now divide by 2: $$ y = -\frac{1}{2}x + 2 $$

From this, we see that the slope ($m$) of the original line is $-\frac{1}{2}$.

2. Use the point-slope form for the new line

Since we want a new line that is parallel to the original line, it will have the same slope of $-\frac{1}{2}$. We will use the point-slope form of a line: $$ y - y_1 = m(x - x_1) $$

Here, $(x_1, y_1) = (0, -4)$ and $m = -\frac{1}{2}$.

Plugging in the values: $$ y - (-4) = -\frac{1}{2}(x - 0) $$

3. Simplify the equation

Now we simplify: $$ y + 4 = -\frac{1}{2}x $$ Subtract 4 from both sides: $$ y = -\frac{1}{2}x - 4 $$

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