Question

which equation represents a line which is parallel to the line $2x + y = -8$?

answer

$\circ$ $y = 2x - 1$ $\circ$ $y = -2x + 1$
$\circ$ $y = \frac{1}{2}x - 6$ $\circ$ $y = -\frac{1}{2}x - 5$

Explanation:

Step1: Find slope of given line

Rewrite \(2x + y = -8\) in slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept).
Subtract \(2x\) from both sides: \(y=-2x - 8\). So the slope of the line \(2x + y=-8\) is \(m=-2\).

Step2: Determine slope of parallel line

Parallel lines have the same slope. So we need to find the equation of the line with slope \(m = - 2\).

Check the slopes of the given options:

• For \(y = 2x-1\), slope \(m = 2\) (not equal to - 2).
• For \(y=-2x + 1\), slope \(m=-2\) (equal to the slope of the given line).
• For \(y=\frac{1}{2}x-6\), slope \(m=\frac{1}{2}\) (not equal to - 2).
• For \(y =-\frac{1}{2}x-5\), slope \(m =-\frac{1}{2}\) (not equal to - 2).

Answer:

\(y=-2x + 1\)