Question

Which equation represents a line that is parallel to the line with equation y = 2x + 1? Select all that apply.
A. y = 2x – 8
B. y = –2x + 1
C. 2x + y = 7
D. –2x + y = 2
E. –2x – y = 9

Answer 1

To determine which equations represent a line that is parallel to the line given by the equation \(y = 2x + 1\), we need to recall that parallel lines have the same slope.

The slope of the line \(y = 2x + 1\) is \(2\).

Now, let's analyze each given equation to see if they also have a slope of \(2\):

A. \(y = 2x - 8\)
- The slope is \(2\). This line is parallel.

B. \(y = -2x + 1\)
- The slope is \(-2\). This line is not parallel.

C. \(2x + y = 7\)
- Rearranging to slope-intercept form:
\(y = -2x + 7\)
The slope is \(-2\). This line is not parallel.

D. \(-2x + y = 2\)
- Rearranging to slope-intercept form:
\(y = 2x + 2\)
The slope is \(2\). This line is parallel.

E. \(-2x - y = 9\)
- Rearranging to slope-intercept form:
\(-y = 2x + 9\) or \(y = -2x - 9\)
The slope is \(-2\). This line is not parallel.

Based on this analysis, the equations that represent lines parallel to \(y = 2x + 1\) are:

**A. \(y = 2x - 8\)**
**D. \(-2x + y = 2\)**