Question

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

Answer 1

Answer:

x = 5

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,

$m=\frac{y_1-y_2}{x-x}_{}=\frac{y_1-y_2}{0}_{}$

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.