Answer:
The equation of a vertical line that passes through the point \((3,-3)\) is
\(x=3\)
Step-by-step explanation:
The equation of a generic line is :
\(y=ax+b\) (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 ⇒
\(y=a.(0)+b\\y=b\)
Where ''b'' is still a real number. The equation \(y=b\) gives us the family of all horizontal lines which cut the y-axis in the point \((0,b)\)
Now, if ''y'' is equal to 0 ⇒
\(0=ax+b\)
\(ax=-b\)
\(x=\frac{-b}{a}\)
If we replace ''\(\frac{-b}{a}\)'' by ''c'' (where ''c'' is a real number), the equation \(x=c\) gives us the family of all vertical lines which cut the x-axis in the point \((c,0)\).
If we want to write the equation of a vertical line we can write
\(x=c\) 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 \((3,0)\) ⇒ It equation will be \(x=3\)
