Question

Find the slope then write an equation for the line that passes through each pair of points (5,-2) (5,18)

Answer 1

To obtain the equation of the line that passes through these points, you can first obtain the slope of the line, using the formula

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}`

And then use the point-slope formula

`y-y_1=m(x-x_1)`

So, in this case, you have

`\begin{gathered} (x_1,y_1)=(5,-2) \\ (x_2,y_2)=(5,18) \end{gathered}`
`\begin{gathered} m=(18-(-2))/(5-5) \\ m=(18+2)/(0) \\ m=(20)/(0) \end{gathered}`

Since the division by 0 is an indeterminacy then the slope of this line is not defined and these points pass through a vertical line that passes through x = 5, as you can see in the graph

Therefore, the slope of the line is undefined and the equation of the line that passes through these pair of points is

`x=5`