Question

What is the equation of the line that passes through the given points (2,3) and (2,5)

Answer 1

The equation of a line that passes through two points is expressed as

`\begin{gathered} y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1) \\ where \\ (x_1,y_1)\text{ and} \\ (x_2,y_2)\text{ are the coordinates of the points } \\ through\text{ which the line passes} \end{gathered}`

Given that the line passes through the points (2,3) and (2, 5), this implies that

`\begin{gathered} x_1=2 \\ y_1=3 \\ x_2=2 \\ y_2=5 \end{gathered}`

By substitution, we have

`\begin{gathered} y-3=(5-3)/(2-2)(x-2) \\ \Rightarrow y-3=(2)/(0)(x-2) \\ multiply\text{ through by zero} \\ 0(y-3)=2(x-2) \\ \Rightarrow0=2x-4 \\ add\text{ 4 to both sides} \\ 0+4=2x-4+4 \\ \Rightarrow4=2x \\ divide\text{ both sides by the coefficient of x, which is 2} \\ (4)/(2)=(2x)/(2) \\ \Rightarrow x=2 \\ \end{gathered}`

Hence, the equation of the line that passes through the given points (2,3) and (2,5) is

`x=2`