Answer:
The slope of the line is 0.
Step-by-step explanation:
Let the coordinates of point P be ([tex]x_{1}, \ y_{1}[/tex]) and point Q be ([tex]x_{2}, \ y_{2}[/tex]), then the slope of the line passing through both points P and Q is
[tex]\text{slope} \ = \ \displaystyle\frac{y_{1} \ - \ y_2}{x_{1} \ - \ x_{2}}[/tex].
Therefore, the slope of the line that passes through the points (3, 1) and (0, 1) is
[tex]\text{slope} \ = \ \displaystyle\frac{1 \ - \ 1}{3 \ - \ 0}[/tex]
[tex]\text{slope} \ = \ \displaystyle\frac{0}{3}[/tex]
[tex]\text{slope} \ = \ 0[/tex].
Notice that both points, in this case, have the same y-coordinate which is 1. This indicates that the line is a horizontal line parallel to the x-axis which has a slope of 0.
If the two points in which a line passes through share the same x-coordinate, the resulting line is a vertical line parallel to the y-axis which has an undefined slope since
[tex]\text{slope} \ = \ \displaystyle\frac{\text{number}}{0}[/tex],
where the x-coordinate of both points cancels out to give a zero in the denominator. (Remember you cannot divide a number by zero!)