Find the equation of the line that passes through the points (2,3) and (2,6).

Question:

Find the equation of the line that passes through the points (2,3) and (2,6).

Vertical Line:

A vertical line is the line whose slope is undefined. The equation of a vertical line passing through a point {eq}\displaystyle { (a,b) } {/eq} is,

{eq}\displaystyle { x = a } {/eq}

where, 'a' is the x-coordinate.

Slope of a line passing through 2 points {eq}\displaystyle { (x_1,y_1) \ \text{and} \ (x_2,y_2) } {/eq} is given as:

{eq}\displaystyle { m = \frac{y_2-y_1}{x^2-x_1} } {/eq}

Given 2 points:

{eq}\displaystyle { P_1 = (2,3) \\ P_2 = (2,6) } {/eq}

Slope of the line passing through these points is,

{eq}\displaystyle { m = \frac{6-3}{2-2} = \frac{3}{0} = \text{Undefined} } {/eq}

It signifies that the line is vertical and therefore the line equation is,

{eq}\displaystyle { x = 2 } {/eq}