To determine a line that is parallel to the given line [tex]\(8x + 2y = 12\)[/tex], we need to follow these steps:
1. Find the slope of the given line:
- Start by rewriting the equation in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- Begin with the original equation [tex]\(8x + 2y = 12\)[/tex].
- Solve for [tex]\(y\)[/tex]:
[tex]\[
2y = -8x + 12
\][/tex]
[tex]\[
y = -4x + 6
\][/tex]
- From this form, it's clear that the slope [tex]\(m\)[/tex] of the given line is [tex]\(-4\)[/tex].
2. Determine the form of a parallel line:
- Lines that are parallel have the same slope. So, any line parallel to the given line will also have a slope of [tex]\(-4\)[/tex].
- The general form of a line with slope [tex]\(-4\)[/tex] can be written as [tex]\(y = -4x + c\)[/tex], where [tex]\(c\)[/tex] is any constant.
3. Specify a parallel line:
- For simplicity, let's choose [tex]\(c = 0\)[/tex] which is a convenient choice.
- Thus, a parallel line can be written as [tex]\(y = -4x\)[/tex].
Therefore, a line that is parallel to the line [tex]\(8x + 2y = 12\)[/tex] is [tex]\(y = -4x\)[/tex].
