Question

Which of the following slopes of a line passes through points (3, 1) and (o, 1)?

5
3
0
None of these choices

Answer 1

The slope of the line is 0.

Explanation:

Let the coordinates of point P be (
`x_(1), \ y_(1)`) and point Q be (
`x_(2), \ y_(2)`), then the slope of the line passing through both points P and Q is

`\text{slope} \ = \ \displaystyle(y_(1) \ - \ y_2)/(x_(1) \ - \ x_(2))`.

Therefore, the slope of the line that passes through the points (3, 1) and (0, 1) is

`\text{slope} \ = \ \displaystyle(1 \ - \ 1)/(3 \ - \ 0)`

`\text{slope} \ = \ \displaystyle(0)/(3)`

`\text{slope} \ = \ 0`.

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

`\text{slope} \ = \ \displaystyle\frac{\text{number}}{0}`,

where the x-coordinate of both points cancels out to give a zero in the denominator. (Remember you cannot divide a number by zero!)