Find the slope and the equation of the line passing through the points:

The slope of the equation can be calculated using

$\mathrm{m}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}} \Rightarrow \frac{\mathrm{b}-\mathrm{b}}{-\mathrm{a}-\mathrm{a}}=0$

m = 0 (Horizontal line)

Now using two point form of the equation of a line

$\mathrm{y}-\mathrm{y}_{1}=\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\left(\mathrm{x}-\mathrm{x}_{1}\right)$

$y-b=0(x-a)$

$y=b$

So, required equation of line is y = b