Question

The line with a undefine slope and passing through the point E(5,-3)

Answer 1

x = 5

Step-by-step explanation:

A vertical line has an undefined slope because according to the definition

`m=\frac{\text{rise}}{\text{run}}`

Any two points chosen on the line have the same x-coordinate but different y-coordinates; therefore,

`m=(y_1-y_2)/(x-x)_{}=(y_1-y_2)/(0)_{}`

Since there is a zero in the denominator, the slope is undefined.

The vertical line passes through only one value of x; therefore, the equation can be written as

`x=a`

where a is any number.

Now in our case, our line passes through x = 5; therefore, the equation of the vertical line is

`x=5.`

The graph of the equation is given below.