Question

Which line is parallel to the line 8x + 2y = 12?

On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 4).

On a coordinate plane, a line goes through (negative 1, 1) and (3, 0).

On a coordinate plane, a line goes through (negative 2, 2) and (negative 1, negative 2).

On a coordinate plane, a line goes through (negative 3, 2) and (1, 3).

Answer 1

To determine which line is parallel to the line represented by the equation \(8x + 2y = 12\), we first need to find the slope of this line.

1. Rewrite the equation in slope-intercept form \(y = mx + b\):
\[
2y = -8x + 12
\]
\[
y = -4x + 6
\]
The slope \(m\) of the line is \(-4\).

2. Lines are parallel if they have the same slope. Thus, we need to check the slopes of the given lines.

**Line 1:** Through points \((-2, -4)\) and \((0, 4)\):
\[
\text{slope} = \frac{4 - (-4)}{0 - (-2)} = \frac{4 + 4}{0 + 2} = \frac{8}{2} = 4
\]

**Line 2:** Through points \((-1, 1)\) and \((3, 0)\):
\[
\text{slope} = \frac{0 - 1}{3 - (-1)} = \frac{-1}{3 + 1} = \frac{-1}{4}
\]

**Line 3:** Through points \((-2, 2)\) and \((-1, -2)\):
\[
\text{slope} = \frac{-2 - 2}{-1 - (-2)} = \frac{-4}{-1 + 2} = \frac{-4}{1} = -4
\]

**Line 4:** Through points \((-3, 2)\) and \((1, 3)\):
\[
\text{slope} = \frac{3 - 2}{1 - (-3)} = \frac{1}{1 + 3} = \frac{1}{4}
\]

Now we summarize the slopes:
- Line 1: \(4\)
- Line 2: \(-\frac{1}{4}\)
- Line 3: \(-4\) (this slope matches the slope of the original line)
- Line 4: \(\frac{1}{4}\)

Therefore, the line that is parallel to \(8x + 2y = 12\) is the line that goes through \((-2, 2)\) and \((-1, -2)\).