Question

Which equation represents a line which is parallel to the line 2x+y=-8?A. y=− 1/2 x−4B. y=−2x+5C. y=2x+3D. y= 1/2x+2

Answer 1

Two lines that are parallel have the same slope. In its slope-intersect form, we can write the equation of a line with slope m and y-intercept b as:

`y=mx+b`

Step 1

Write the given equation in slope-intercept form and identify its slope m.

`\begin{gathered} 2x+y=-8 \\ \\ 2x+y-2x=-2x-8 \\ \\ y=-2x-8 \end{gathered}`

Thus:

`m=-2`

Step 2

Find the equation with the same slope m = -2. We need to identify which of them has -2 multiplying the variable x.

Answer

From the given options, the only one with the same slope m = -2, therefore parallel to the given line, is:

`y=-2x+5\text{ (option B)}`