Question

Find the equation of the line that passes through the pair of points.

(1,5), (1, - 3)

Answer 1

x = 1

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (1, 5) and (1, -3).

Substitute:

`m=\dfrav{-3-5}{1-1}=(-8)/(0)\ \bold{!}`

Dividing by zero is not possible.

The slope does not exist.

Conclusion: this is a vertical line with the equation x = a

From the points

(1, 5) → x = 1, y = 5

(1, -3) → x = 1, y = -3

we have the equation x = 1.