Which equation represents a line that is parallel to \(y = -2x + 7\)?

To determine which equation represents a line that is parallel to (y = -2x + 7), it's essential to understand what it means for two lines to be parallel. Lines are parallel when they have the same slope.

The slope-intercept form of a linear equation is (y = mx + b), where (m) is the slope and (b) is the y-intercept. In the given equation (y = -2x + 7), the slope is (-2). Therefore, any line that is parallel to this line must also have a slope of (-2).

Now, examining the available choices:

• The first equation, (y = -2x - 3), has a slope of (-2). This means that it has the same slope as the original line, so it is indeed parallel.

• The second equation, (y = 2x + 7), has a slope of (2), which does not match the original slope.

• The third equation, (y = -\frac{1}{2}x + 7), has a slope of (-\frac{1}{2}), which is also