Answer:
The equation of a vertical line that passes through the point [tex](3,-3)[/tex] is
[tex]x=3[/tex]
Step-by-step explanation:
The equation of a generic line is :
[tex]y=ax+b[/tex] (I)
Where ''a'' and ''b'' are real numbers.
The horizontal and vertical lines are particular cases of the equation (I).
If ''x'' is equal to 0 ⇒
[tex]y=a.(0)+b\\y=b[/tex]
Where ''b'' is still a real number. The equation [tex]y=b[/tex] gives us the family of all horizontal lines which cut the y-axis in the point [tex](0,b)[/tex]
Now, if ''y'' is equal to 0 ⇒
[tex]0=ax+b[/tex]
[tex]ax=-b[/tex]
[tex]x=\frac{-b}{a}[/tex]
If we replace ''[tex]\frac{-b}{a}[/tex]'' by ''c'' (where ''c'' is a real number), the equation [tex]x=c[/tex] gives us the family of all vertical lines which cut the x-axis in the point [tex](c,0)[/tex].
If we want to write the equation of a vertical line we can write
[tex]x=c[/tex] and then we will need to find the value of ''c''. Our line must passes through the point (3,-3). If the second coordinate is 0 then the vertical line will intersect the x-axis at [tex](3,0)[/tex] ⇒ It equation will be [tex]x=3[/tex]
