Question

Which equation represents a line which is parallel to the line y, equals, 8, x, minus, 4y=8x−4?

Answer 1

To determine a line that is parallel to the line represented by the equation \(8x - 4y = 8\), we first need to put the equation in slope-intercept form, \(y = mx + b\), where \(m\) represents the slope.

Let's rearrange the given equation:

1. Start with the equation:
\[
8x - 4y = 8
\]

2. Isolate \(y\):
\[
-4y = -8x + 8
\]

3. Divide by \(-4\) to solve for \(y\):
\[
y = 2x - 2
\]

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

Parallel lines have the same slope, so a line parallel to this one will also have a slope of \(2\).

Using the slope-intercept form, a general equation for a line parallel to the given line can be expressed as:
\[
y = 2x + b
\]
where \(b\) is any real number representing the y-intercept.

For example, if we choose \(b = 1\), a specific parallel line would be:
\[
y = 2x + 1
\]

You can choose any value for \(b\) to create different parallel lines.