Question

Find the slope of AB with the points lying on A(3, 2), (−8, 2) when the line AB parallel to X-axis? Why?

Answer 1

slope of line joining points $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$m=\frac{y_2-y_1}{x_2-x_1}$

so, slope of line joining points A(3,2) and B(-8,2) is given by m = (2 - 2)/(-8 - 3) = 0/-11 = 0
e.g., slope of line AB , m = 0

so, equation of line : $(y-y_1)=m(x-x_1)$
so, equation of line AB : (y - 2) = 0(x + 8) = 0
y = 2 , if you draw graph of y = 2 , you will see it is parallel to X-axis.

actually, if slope of any line = 0 then it will be parallel to X-axis. here slope of line AB = 0
that's why it is parallel to X-axis.

Answer 2

In the attachment I have answered this problem.   Concept:  Slope of line joining two points is   (y2 - y1) / (x2 - x1)   Parallel lines have same slopes   See the attachment for detailed solution