The equation of line m is y = ax + b. Which could be the equation of line n?

To determine which equation could represent line n, we need to understand that lines m and n are related through their slopes. Line m has a slope of (a).

If line n has a slope that is the negative reciprocal of (a), it would be perpendicular to line m. For instance, if line m has a slope of (a), then line n would need to have a slope of (-frac{1}{a}) to be perpendicular.

Looking at the options provided, we can isolate the slopes:

1. (y = -frac{1}{2} a(x – 5) + b) has a slope of (-frac{1}{2} a).
2. (y = -frac{1}{2} ax + b + 5) has a slope of (-frac{1}{2} a).
3. (y = frac{1}{2} a(x + 5) + b) has a slope of (frac{1}{2} a).
4. (y = frac{1}{2} ax + b – 5) has a slope of (frac{1}{2} a).

The only options that offer a negative slope are the first two. However, without knowing the specific value of (a) in relation to perpendicularity, we can’t definitively assert that they represent perpendicular lines.