Question

Write the equation of the line that passes through the points (2,8) and(2,9). Put your answer in fully reduced point-slope form, unless it is avertical or horizontal line.

Answer 1

Concept

Use the equation of a line for two-point forms below to find the equation of a line.

$\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}$

Step 1: Represent each value of the coordinate.

Point (2 , 8) and (2, 9)

$\begin{gathered} x_1\text{ = 2} \\ y_1\text{ = 8} \\ x_2\text{ = 2} \\ y_2\text{ = 9} \end{gathered}$

Step 2: Substitute all the value in the equation

$\begin{gathered} \frac{y\text{ - 8}}{x\text{ - 2}}\text{ = }\frac{9\text{ - 8}}{2\text{ - 2}} \\ \frac{y\text{ - 8}}{x\text{ - 2}}\text{ = }\frac{1}{0} \\ \text{Cross multiply} \\ (x\text{ - 2) x 1 = (y - 8) x 0} \\ x\text{ - 2 = 0} \\ x\text{ = 2} \end{gathered}$

Step 3: Final answer

x = 2 and it is vertical