Answer:
[tex]x_2=x_1[/tex]
Step-by-step explanation:
We were given the slope formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
This line is vertical if the denominator is zero.
That is when [tex]x_2-x-1=0[/tex]
This implies that;
[tex]x_2=x_1[/tex]
Justification;
When [tex]x_2=x_1[/tex], then, the line passes through;
[tex](x_1,y_1)[/tex] and [tex](x_1,y_2)[/tex]
The slope now become
[tex]m=\frac{y_2-y_1}{x_1-x_1}=\frac{y_2-y_1}{0}[/tex]
The equation of the line is
[tex]y-y_1=\frac{y_2-y_1}{0}(x-x_1)[/tex]
This implies that;
[tex]0(y-y_1)=(y_2-y_1)(x-x_1)[/tex]
[tex]0=(y_2-y_1)(x-x_1)[/tex]
[tex]\frac{0}{y_2-y_1}=(x-x_1)[/tex]
[tex]0=(x-x_1)[/tex]
[tex]x=x_1[/tex]... This is the equation of a vertical line.
